23. [Perimeter / Area]
Skill 23.1
•
•
•
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the perimeter of polygons (1).
Convert all measurements to the same unit.
Find and label the length of all sides.
Add together all side lengths.
Hints: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Q. Find the perimeter of the scalene triangle in
centimetres.
110 cm
A. 650 mm = 650 ÷ 10 cm
Convert mm to cm
= 65 cm
P = 65 cm + 110 cm + 70 cm
P = 245 cm
70 cm
650 mm
a)
b) Find the perimeter of the trapezium.
Find the perimeter of the rectangle.
1.9 m
13 mm
33 mm
13 mm
33 mm
33 mm
0.7 m
P
= 33 + 33 + 13 + 13
.......................................................................................................
= 66 + 26
=
...............................................................
c)
P = 1.5 +
.......................................................................................................
=
mm
15 mm
P
=
.......................................................................................................
=
...............................................................
e)
P
=
......................................................................................................
=
...............................................................
page 259
m
18 cm
.......................................................................................................
P
=
=
...............................................................
mm
What is the perimeter of a regular heptagon
with sides measuring 14 m?
=
m
30 cm
240 mm
=
=
...............................................................
d) Find the perimeter of the right-angled triangle
in millimetres.
Find the perimeter of the kite.
6 mm
0.6 m
1.5 m
13 mm
f)
What is the perimeter in centimetres of a
rhombus with a side length measuring 125 mm?
.......................................................................................................
P
=
=
...............................................................
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© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.1
g) What is the perimeter in centimetres of an
isoceles triangle with congruent sides of 15 m
and the other side measuring 1.5 m?
i)
h) Find the perimeter in centimetres of a
parallelogram with side lengths measuring
202 cm and 100 mm.
.......................................................................................................
.......................................................................................................
P
=
=
...............................................................
P
=
=
...............................................................
The smallest ever postage stamp came from
Columbia. Rectangular, it measured 7.85 mm
by 9.4 mm. What was its perimeter in cm?
j)
P
=
.......................................................................................................
=
=
=
=
...............................................................
Lisa’s backyard is a rectangle measuring 28 m
in length and 12 m in width. What will the
perimeter of the backyard be?
P
=
.......................................................................................................
=
An Australian $20 note measures 14.4 cm by
6.5 cm. What is its perimeter in
millimetres?
P
=
.......................................................................................................
...............................................................
k)
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the perimeter of polygons (2).
=
m
...............................................................
m) Find the perimeter of the trapezium.
l)
Find the perimeter in centimetres of a kite
with side lengths measuring 180 cm and
750 mm.
.......................................................................................................
P
=
=
...............................................................
n) Find the perimeter of the triangle.
100 m
9 mm
40
m
14 mm
13 mm
7 mm
20 m
P
=
.......................................................................................................
=
=
m
...............................................................
o) Write an algebraic expression for the perimeter
P of the heptagon. [Express the answer in terms of r.]
P
=
.......................................................................................................
=
=
mm
...............................................................
p) Write an algebraic expression for the perimeter
P of the rectangle. [Express the answer in terms of s.]
r
s
3s
P
=
.......................................................................................................
=
...............................................................
page 260
P=
P
=
.......................................................................................................
=
...............................................................
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P=
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.2
•
•
Find and label the length of all sides.
OR
Add together all side lengths.
• Manipulate shapes to
Hints: Sides marked with a dash ( ) are of equal length.
become rectangles by
Sides marked with two dashes ( ) are of equal length etc.
pushing out inverted corners.
Q. Find the perimeter of the shape.
4.5 m
4m
Find unknown
side lengths
10 m
unknown sides:
6 + dash + dash = 10 m
So each dashed side = 2 m
6m
a)
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Calculating the perimeter of composite shapes.
A. P = 10 + 4.5 + 2 + 4 + 2 + 4 + 6 + 4.5
= 14.5 + 8 + 10 + 4.5
= 37 m
4.5 m
OR
P = 10 + 10 + 8.5 + 8.5
10 m
= 20 + 17
shape becomes
= 37 m
4m
6m
a rectangle
8.5 m
b) Find the perimeter of the shape.
Find the perimeter of the shape.
3 mm
3.5 mm
5 mm
7 mm
P
= 3.5 + 7 + 7 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5
.......................................................................................................
= 14 + 24.5
=
=
mm
...............................................................
c)
P=
.......................................................................................................
Find the perimeter in centimetres around the
coloured background of this Tongan flag.
=
...............................................................
mm
d) Find the perimeter of the shape.
0.6 cm
1.3 cm
60 cm
75 cm
125 cm
P
=
.......................................................................................................
=
=
=
cm
...............................................................
e)
P=
.......................................................................................................
f)
Find the perimeter of the shape.
=
...............................................................
cm
Find the perimeter of the shape.
4m
5 cm
4 cm
3.5 m
2.5 m
2.5 m
10 cm
P
=
.......................................................................................................
=
=
...............................................................
page 261
m
P=
.......................................................................................................
=
=
...............................................................
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cm
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.3
•
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Calculating the circumference of circles.
Substitute known values into the formula.
Hints: The diameter of a circle is equal to twice the radius.
π (pi) gets its value because the diameter of any circle
fits approximately 3.14 times around the circumference.
Circumference of a circle
C = 2 × π × radius
C = 2πr
OR
C = π × diameter
C = πd
22
where π ≈ 3.14... or
7
22
Q. Using C = 2πr where π ≈ , find the
7
length of the semicircle.
A. C = 2πr
22
Simplify: ÷ 7
=2×
×7
7
= 44
1
1
C = × 44 = 22 m
O
2
7m
b) Using C = 2πr where π ≈ 3.14, find the
circumference of the circle.
Using C = 2πr where π ≈ 3.14, find the
circumference of the circle.
2m
10
m
m
a)
2
O
O
C
= 2πr
.......................................................................................................
C
= πd where d = 10
.......................................................................................................
= 10 × 3.14
=
...............................................................
22
=
=
...............................................................
m
d) Using π ≈ 3.14 find the length of the
semicircle.
Using C = 2πr where π ≈ , find the
7
circumference of the circle.
56
cm
c)
mm
O
30 m
O
C
=
.......................................................................................................
=
=
...............................................................
e)
C
=
.......................................................................................................
cm
1
2
f)
The diameter of a circular discus is 2.5 m.
Using π ≈ 3.14 what is the circumference?
C
=
=
...............................................................
Using π ≈ 3.14 find the length of the
quarter circle.
C
=
.......................................................................................................
=
=
...............................................................
8 mm
O
m
C
=
.......................................................................................................
1
4
page 262
m
C
=
=
...............................................................
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mm
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.4
•
•
•
•
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the perimeter of composite circular shapes (1).
Find and label the length of all sides.
Break the shape into workable parts.
For circular shapes substitute known values into the formula
for the circumference:
Hint: Consider 2 congruent semicircles equal 1 full circle.
Add together all side lengths.
Hints: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Q. Find the perimeter of the shape.
(Use π ≈ 3.14)
Circumference of a circle
C = 2πr = πd
A
A.
5 mm
B
⇒
5 mm
D
C = 2πr where r = 10
= 2 × 3.14 × 10 = 62.8
A = 62.8 ÷ 2 = 31.4
C = 2πr where r = 5
= 2 × 3.14 × 5 = 31.4
B = 31.4 ÷ 2 = 15.7
C = πd where d = 5
D = 3.14 × 5 = 15.7
shape = 31.4 + 15.7 + 15.7
= 62.8 mm
Using C = 2πr where π ≈ 3.14, find the
perimeter around the outside of the first lane
of an athletics track.
semicircle B circle D
a)
semicircle A
5 mm
b) Find the perimeter of the shape.
22
(Use π ≈ )
7
Standard 400 m athletics track
(1 lane shown)
1.2 m
O
85 m
1.
4
O'
36.4 m
cm
Consider 2 semicircles
as 1 circle
C
= 2πr where r = 36.4 + 1.2 = 37.6
.......................................................................................................
C
= 2πr
.......................................................................................................
C
= 2 × 3.14 × 37.6 = 236.128
.......................................................................................................
.......................................................................................................
85 + 85 = 170
.......................................................................................................
P
= 236.128 + 170 =
........................................................
page 263
406.128 m
.......................................................................................................
P
=
=
...............................................................
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cm
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.4
c)
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the perimeter of composite circular shapes (2).
d) Find the perimeter of the shape.
22
(Use π ≈ )
Using C = 2πr where π ≈ 3.14, find the
perimeter of the shape.
7
10 mm
14 m
5 mm
C
= 2πr where r =
.......................................................................................................
C
= 2πr
.......................................................................................................
C
=
.......................................................................................................
.......................................................................................................
P
=
.......................................................................................................
P
=
.......................................................................................................
=
mm
=
...............................................................
e)
=
f)
Using C = 2πr where π ≈ 3.14, find the
perimeter of the shape.
m
=
...............................................................
Find the perimeter of the shape.
22
(Use π ≈ )
7
9 mm
34 cm
8 mm
20 cm
20 mm
.......................................................................................................
.......................................................................................................
P
=
.......................................................................................................
.......................................................................................................
=
mm
=
...............................................................
g) Write an algebraic expression for the perimeter
P of the shape. [Express the answer in terms of r and π.]
cm
...............................................................
h) Write an algebraic expression for the
circumference P of the outer circle.
[Express the answer in terms of k and π.]
k
k
r
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
...............................................................
page 264
P=
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P=
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.5
•
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the area of squares and rectangles.
Substitute known values
into the appropriate formula.
Area of a square
Area of a rectangle
w = width
l = length
A =l×l
=l2
l = length
A =l×w
= lw
Q. A boxing ring is a square with side length
5.2 m. What is the area of the ring?
A. A = l 2
= 5.2 × 5.2 m
= 27.04 m 2
a)
b) Find the area of the square.
What is the area of a rectangular billiard table
with a length of 3.7 m and a width of 1.9 m?
13 cm
A
=l×w
.......................................................................................................
= 3.7 × 1.9
=
...............................................................
A=
m2
.......................................................................................................
=
=
...............................................................
c)
d) A baseball diamond is a square of side length
of approximately 27 m. What is its area?
Find the area of the rectangle.
11 mm
A=
4.3 mm
.......................................................................................................
=
=
=
e)
A
=l×w
.......................................................................................................
=
=
m2
g) What is the perimeter of a square with an area
of 400 cm 2?
length
=
.......................................................................................................
P
=
=
...............................................................
page 265
m2
mm 2
The rectangular grounds of the Taj Mahal are
360 m long and 260 m wide. What is its
area?
...............................................................
=
...............................................................
A
=
.......................................................................................................
...............................................................
cm 2
cm
f)
A rectangular badminton court measures
approximately 13.5 m long and 6 m wide.
What is its area?
A=
.......................................................................................................
=
=
...............................................................
m2
h) Paddy’s rectangular iPod screen has an area of
720 mm 2. What is the perimeter of the screen,
if the length measures 30 mm?
width =
.......................................................................................................
P
=
=
...............................................................
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Skill 23.6
•
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Calculating the area of triangles.
Substitute known values into the formula:
Area of a triangle
A =
h = height
=
b = base
Q. Find the area of the scalene triangle.
A. A =
10 cm
=
1
×b×h
bh
1
bh
2
5
1
× 10
2
Simplify: ÷ 2
×7
= 35 cm 2
7 cm
a)
1
2
1
2
b) Find the area of the right-angled triangle.
Find the area of the right-angled triangle.
8 mm
5m
10 mm
18 m
1
bh
2
.......................................................................................................
1
bh
2
.......................................................................................................
A=
1
=
× 18 × 5
2
...............................................................
=
c)
A=
=
m2
=
mm 2
...............................................................
d) Find the area of the scalene triangle.
Find the area of the isoceles triangle.
4 cm
12
mm
6
cm
8 mm
1
bh
2
.......................................................................................................
A=
=
=
Plot the points A(−6,2), B(−2,6) and C(5,2)
and use them to find the area of ΔABC.
B
A
=
=
cm 2
...............................................................
f)
Plot the points A(−2,3), B(3,3) and C(−2,−3)
and use them to find the area of ΔABC.
Y
Y
7
6
5
4
3
2
1
4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5
page 266
.......................................................................................................
mm 2
...............................................................
e)
A=
3
2
1
−4 −3 −2 −1 0 1
−1
2
3
4
X
−2
X
−3
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Skill 23.7
•
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MM6.1 1 1 2 2 3 3 4 4
Calculating the area of parallelograms.
Substitute known values into the formula.
Area of a parallelogram
h = height
b = base
A =b×h
= bh
A. A = bh
= 2.5 × 3.5 m
= 8.75 m 2
Q. Find the area of the parallelogram.
2.5 m
3.5 m
a)
b) Find the area of the parallelogram.
Find the area of the parallelogram.
25 cm
7 cm
14 cm
11 cm
A
= bh
.......................................................................................................
= 14 × 25
=
...............................................................
c)
A=
.......................................................................................................
cm 2
=
=
...............................................................
cm 2
d) Find the area of the parallelogram.
Find the area of the parallelogram.
2.5 mm
30 cm
17 cm
1.2 mm
A
=
.......................................................................................................
=
=
...............................................................
e)
A=
.......................................................................................................
cm 2
=
f)
Find the area of the parallelogram.
=
...............................................................
mm 2
Find the area of the parallelogram.
21 mm
5.5 m
13 mm
2m
A
=
.......................................................................................................
=
=
...............................................................
page 267
m2
A=
.......................................................................................................
=
=
...............................................................
www.mathsmate.co.nz
mm 2
© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.8
•
Substitute known values into the formula.
Area of a rhombus or kite
A =
b
a
b
OR
Q. Find the area of the kite.
1
2
×a×b
(where a is the long diagonal
and b is the short diagonal)
= 1 ab
a
2
A. A =
=
m
1
ab
2
1
× 7.5
2
×3
= 11.25 m 2
3m
7.5
a)
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Calculating the area of rhombi and kites.
b) Find the area of the rhombus.
Find the area of the kite.
8m
10 cm
5m
27.5 cm
1
ab
2
.......................................................................................................
1
ab
2
.......................................................................................................
A=
1
=
2
...............................................................
= × 27.5 × 10
c)
A=
=
cm 2
=
m2
...............................................................
d) Find the area of the kite.
Find the area of the rhombus.
30.5 cm
16 mm
20 cm
1
A=
.......................................................................................................
.......................................................................................................
=
=
Plot the points A(0,4), B(2,2), C(0,−3) and
D(−2,2) and use them to find the area of the
kite ABCD.
Y
4
=
cm 2
...............................................................
e)
7 mm
A = 2 ab
A
f)
1
−4 −3 −2 −1 0 1
−1
7
6
5
4
3
2
1
B
2
3
4
mm 2
Plot the points A(−4,6), B(−2,3), C(−4,0) and
D(−6,3) and use them to find the area of the
rhombus ABCD.
Y
3
2
=
...............................................................
X
−2
−6 −5 −4 −3 −2 −1 0 1
−3
X
−4
page 268
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© Maths Mate 5.2/6.1 Skill Builder 23
Skill 23.9
•
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MM6.1 1 1 2 2 3 3 4 4
Calculating the area of trapeziums.
Substitute known values into the formula.
Area of a trapezium
A =
b
h
a
1
2
× (a + b) × height
(where a and b
are the parallel
side lengths)
= 1 (a + b)h
2
Q. Find the area of the trapezium.
A. A =
1.5 mm
=
=
1 mm
×1
= 2.75 mm 2
4 mm
a)
1
(a + b)h
2
1
× (4 + 1.5)
2
1
× 5.5
2
b) Find the area of the trapezium.
Find the area of the trapezium.
23 m
12 mm
12 m
10 mm
9m
20 mm
1
1
A = (a + b)h = × (23 + 9) × 12
2
2
.......................................................................................................
1
=
2
...............................................................
= × 32 × 12
c)
1
A = (a + b)h =
2
.......................................................................................................
=
m2
=
d) Find the area of the trapezium.
Find the area of the trapezium.
17 cm
20
28 cm
mm 2
...............................................................
15 cm
cm
8 cm
3 cm
1
(a + b)h =
2
.......................................................................................................
A=
=
=
Plot the points A(0,4), B(3,4), C(3,−2) and
D(−4,−2) and use them to find the area of the
trapezium ABCD.
Y
4
A
B
=
f)
7
6
5
4
3
2
1
1
3
4
cm 2
Plot the points A(−4,5), B(4,6), C(4,1) and
D(−4,4) and use them to find the area of the
trapezium ABCD.
Y
3
2
=
...............................................................
2
−4 −3 −2 −1 0 1
−1
=
.......................................................................................................
cm 2
...............................................................
e)
A=
X
−2
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−3
X
−4
page 269
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© Maths Mate 5.2/6.1 Skill Builder 23
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Skill 23.10 Calculating the area of composite shapes (1).
•
•
•
•
Find and label the length of all sides.
Break the shape into workable parts.
Where possible substitute values into a known area formula.
(see skill 23.5, page 265 to skill 23.9, page 269)
Add or subtract the area totals where necessary.
Q. Find the area of the polygon.
A.
3m
8m
3m
+
8m
A
8m
B
6m
=
=
B =
=
=
1
(a + b)h
2
1
× (3 + 8) × 6
2
1
× 11 × 6 = 33
2
1
bh
2
1
×6×8
2
1
× 48 = 24
2
triangle B
A=
trapezium A
6m
6m
shape = A + B = 33 + 24 = 57 m 2
a)
b) Find the area of the polygon.
Find the area of the shape.
15 m
15 m
8 cm
6m
A
A
25 m
20 cm
4m
20 cm
25 m
plus
minus
8 cm
15 m − 4 m
B
B
20 cm
25 m
32 cm
32 − 20 cm
A
= lw
(a rectangle)
.......................................................................................................
= 25 × 15 = 375
.......................................................................................................
A
= l2
.......................................................................................................
=
.......................................................................................................
1
bh (a triangle)
2
.......................................................................................................
1
1
= × 25 × 11 = × 275 = 137.5
2
2
.......................................................................................................
B =
2
shape
= 375 − 137.5 = 237.5 m
...............................................................
shape
=
=
...............................................................
B =
page 270
.......................................................................................................
=
=
=
.......................................................................................................
www.mathsmate.co.nz
cm 2
© Maths Mate 5.2/6.1 Skill Builder 23
MM5.2 1 1 2 2 3 3 4 4
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Skill 23.10 Calculating the area of composite shapes (2).
c)
d) Find the area of the polygon.
Find the area of the shape.
19 mm
30 cm
15 mm
9 mm
18 cm
12 mm
3 mm
A
=
.......................................................................................................
A=
.......................................................................................................
=
=
.......................................................................................................
.......................................................................................................
B
=
.......................................................................................................
.......................................................................................................
B =
=
e)
=
.......................................................................................................
.......................................................................................................
shape
=
=
...............................................................
shape
=
=
...............................................................
mm 2
f)
Find the area of the shape.
18 m
cm 2
Find the area of the polygon.
22 m
5m 6m
15 m
15 m
5m
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
shape
=
=
...............................................................
shape
=
=
...............................................................
m2
g) Write an algebraic expression for the area
A of the shape. [Express the answer in terms of a and b.]
m2
h) Write an algebraic expression for the area
A of the shape. [Express the answer in terms of a and b.]
a
2a
b
b
a
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
.......................................................................................................
A=
A
=
...............................................................
A=
A
=
...............................................................
page 271
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© Maths Mate 5.2/6.1 Skill Builder 23
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MM6.1 1 1 2 2 3 3 4 4
Skill 23.11 Calculating the area of circles.
•
Area of a circle
Substitute known values into the formula:
Hint: The diameter of a circle is equal to twice the radius.
Pi (π) gets its value because the diameter of any
circle fits approximately 3.14 times around the
circumference.
Q. Using A = πr 2 where π ≈ 3.14, find the
area of the circle.
A = π × radius × radius
A = πr2
22
where π ≈ 3.14... or
7
A. A = πr 2 where d = 24, so r = 12
= 3.14 × 12 × 12
= 3.14 × 144
= 452.16 m 2
24 m
O
Using A = πr 2 where π ≈ 3.14, find the
area of the circle.
b) Using A = πr 2 where π ≈ 3.14, find the area
of the circle.
5m
20
m
m
a)
O
O
A
= πr 2 where d = 20 so r = 10 mm
.......................................................................................................
A
= πr 2
.......................................................................................................
= 3.14 × 10 × 10
=
.......................................................................................................
= 3.14 × 100
=
...............................................................
c)
.......................................................................................................
mm 2
Using A = πr 2 where π ≈ 22 , find the area of
7
the circle.
=
=
...............................................................
d) Using π ≈
42 m
find the area of the semicircle.
28 mm
O
O
.......................................................................................................
......................................................................................................
m2
=
...............................................................
e)
22
7
m2
22
Using π ≈
find the area of the quarter
7
circle.
=
...............................................................
f)
mm 2
Using π ≈ 3.14 find the area of the shape.
O
20 m
O
7 cm
.......................................................................................................
=
...............................................................
page 272
cm 2
.......................................................................................................
=
...............................................................
www.mathsmate.co.nz
m2
© Maths Mate 5.2/6.1 Skill Builder 23
MM5.2 1 1 2 2 3 3 4 4
MM6.1 1 1 2 2 3 3 4 4
Skill 23.12 Calculating the area of composite circular shapes (1).
•
•
•
•
Find and label the length of all sides.
Break the shape into workable parts.
Where possible substitute values into a known area formula.
(see skills 23.5 to skill 23.9, pages 265 to 269 and skill 23.11, page 272)
Add or subtract the area totals where necessary.
Q. Use A = πr 2 where π ≈ 3.14, to find the area
of the shaded shape.
A.
B
A
9m
9m
−
9m
7m
×2
7m
11 m
9m
11 m
=
B =
1
(a + b)h
2
1
1
× (18 + 11) × 7 = ×
2
2
1
× 203 × 2 = 203
2
trapezium ×2 B
A=
circle A
A = πr 2 where r = 9
= 3.14 × 9 × 9
= 3.14 × 81
= 254.34
203
shape = A − B = 254.34 − 203 = 51.34 m 2
22
Use A = πr 2 where π ≈ , to find the shaded
7
area.
22
b) Use A = πr 2 where π ≈ , to find the shaded
7
area.
m
a)
A
14
30 cm
14
m
A
30 cm
minus
7 cm
B
14
minus
m
5 cm
B
14 m
14 m
7 cm
7 cm
5 cm
1
bh
(a triangle)
2
......................................................................................................
A=
1
× (5 + 7 + 7 + 5) × 30 = 360
2
......................................................................................................
A = πr 2, r = 14
=
1 2
πr , r = 7
(a semicircle)
2
......................................................................................................
B =
1 22
×
× 7 × 7 = 11 × 7 = 77
2
7
......................................................................................................
=
shape
= 360 − 77
=
.............................................................
page 273
cm
2
(a circle)
......................................................................................................
=
=
......................................................................................................
B = l2
(a square)
......................................................................................................
=
=
......................................................................................................
shape
=
=
.............................................................
www.mathsmate.co.nz
m2
© Maths Mate 5.2/6.1 Skill Builder 23
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Skill 23.12 Calculating the area of composite circular shapes (2).
c)
22
Use A = πr 2 where π ≈ , to find the area of
7
the background colour of the flag of Zaire,
without the central circle.
d) Use A = πr 2 where π ≈ 3.14, to find the area of
the shaded shape.
40 cm
25 cm
20 mm
14 cm
=
=
.......................................................................................................
=
.......................................................................................................
=
=
.......................................................................................................
=
=
.......................................................................................................
=
.......................................................................................................
=
=
.......................................................................................................
shape
=
=
...............................................................
e)
=
.......................................................................................................
cm 2
Use A = πr 2 where π ≈ 3.14, to find the area of
the shaded shape.
=
.......................................................................................................
shape
=
=
...............................................................
f)
mm 2
Use A = πr 2 where π ≈ 3.14, to find the area of
the shaded shape.
m
10 m
4
6m
16 m
=
.......................................................................................................
=
=
=
.......................................................................................................
=
.......................................................................................................
=
=
.......................................................................................................
shape
=
=
...............................................................
page 274
=
.......................................................................................................
m2
=
.......................................................................................................
=
.......................................................................................................
=
=
.......................................................................................................
shape
=
=
...............................................................
www.mathsmate.co.nz
m2
© Maths Mate 5.2/6.1 Skill Builder 23
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Skill 23.12 Calculating the area of composite circular shapes (3).
g) Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
h) Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
of r and π.]
of r, l and π.]
r
r
r
l
r
r
r
B
A
= πr 2 (a circle)
.......................................................................................................
.......................................................................................................
B
= l2
(a square)
.......................................................................................................
.......................................................................................................
= r2
i)
A
A = πr 2
B =
OR r 2(π − 1)
=
.......................................................................................................
.......................................................................................................
2
2
πr
−
r
A
=
shape
=
A
−
B
.........................................................
A=
shape
=
.........................................................
Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
j)
of d and π.]
r
of r and π.]
Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
d
=
=
.......................................................................................................
.......................................................................................................
=
=
.......................................................................................................
.......................................................................................................
=
k)
=
.......................................................................................................
.......................................................................................................
A=
shape
=
.........................................................
A=
shape
=
.........................................................
Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
of a, b and π.]
l)
Write an algebraic expression for the area
A of the shaded shape. [Express the answer in terms
of a, b and π.]
b
b
a
a
A
rectangle =
.......................................................................................................
A
=
triangle
.......................................................................................................
A
semicircle =
.......................................................................................................
A
semicircle 1 =
.......................................................................................................
.......................................................................................................
=
A
semicircle 2 =
.......................................................................................................
A=
shape
=
.........................................................
A=
shape
=
.........................................................
page 275
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© Maths Mate 5.2/6.1 Skill Builder 23
page 276
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© Maths Mate 5.2/6.1 Skill Builder 23