27. [Perimeter]
Skill 27.1
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Finding the perimeter of polygons by measuring their side
lengths.
Measure each side length of the shape.
Add together the side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Q. Use a ruler to find the perimeter of the
isosceles triangle in inches.
A. 1 in. + 1 in. + 0.5 in. Measure the side lengths.
Write down the lengths
= 2.5 in.
next to each side.
sides marked ( ) are equal
0.5 in.
1 in.
a)
Use a ruler to find the perimeter of the
square in inches.
4 × 1.5
=
.............................................................................
c)
in.
Use a ruler to find the perimeter of the
polygon in inches.
=
.............................................................................
page 253
in.
Start
here
b) Use a ruler to find the perimeter of the
rectangle in inches.
=
.............................................................................
in.
d) Use a ruler to find the perimeter of the
scalene triangle in inches.
=
.............................................................................
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in.
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.2
•
Add together the side lengths.
A. 30 mm + 12 mm + 11 mm + 18 mm
= 71 mm
Q. Calculate the perimeter of the
quadrilateral.
30 mm
12 mm
30 mm
18 mm
12 mm
11 mm
a)
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Calculating the perimeter of polygons when all side lengths
are given.
Start
here
18 mm
11 mm
Calculate the perimeter of the
parallelogram.
b) Calculate the perimeter of the trapezoid.
6.5 cm
41 mm
2 cm
18 mm
9 mm
40 mm
2 cm
6.5 cm
6.5 + 2 + 6.5 + 2
=
.............................................................................
c)
cm
Calculate the perimeter of the
quadrilateral.
=
.............................................................................
mm
d) Calculate the perimeter of the
quadrilateral.
4.5 cm
46 mm
2 cm
14 mm
3 cm
8 mm
30 mm
2.5 cm
=
.............................................................................
e)
cm
Calculate the perimeter of the polygon.
24 mm
46 mm
f)
m
2m
16 mm
1
17 mm
16 mm
=
mm
mm
Calculate the perimeter of the polygon.
20 mm
.............................................................................
page 254
=
.............................................................................
15 m
m
43 mm
37 mm
19 mm
=
.............................................................................
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mm
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.3
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MMGreen 1 1 2 2 3 3 4 4
Calculating the perimeter of polygons by recognizing
congruent sides.
Determine and label all side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Add together the side lengths.
Q. Calculate the perimeter of the isosceles
triangle.
A. 1.5 in. + 2.5 in. + 2.5 in.
= 6.5 in.
2.5 in.
2.5 in.
1.5 in.
1.5 in.
2.5 in.
a)
Calculate the perimeter of the regular
pentagon.
14 mm
label all sides
b) Calculate the perimeter of the isosceles
triangle.
39 mm
14 mm
14 mm
14 mm
14 mm
24 mm
14 mm
pentagon - 5 sides
mm
5 × 14
=
.............................................................................
c)
isosceles triangle
has 2 congruent sides
Calculate the perimeter of the regular
octagonal gazebo with side length 4 ft.
=
.............................................................................
mm
d) Calculate the perimeter of the regular
hexagon.
15 mm
ft
=
.............................................................................
e)
Calculate the perimeter of the trapezoid.
6.5 cm
=
.............................................................................
f)
Calculate the perimeter of the
parallelogram.
17 mm
2.5 cm
43 mm
3 cm
=
.............................................................................
page 255
mm
cm
=
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mm
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.4
•
•
Determine and label all side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Add together the side lengths.
Q. What is the perimeter of this Navy
building in California?
25 ft
100 ft
60 ft
175 ft
195 ft
a)
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Calculating the perimeter of polygons using real-life examples.
A. (75 + 100 + 25 + 75 + 50 + 85 + 100 + 25 + 75 + 60) × 2
= 670 × 2
= 1340 ft
100 ft
Redraw half the shape.
25 ft
75 ft
Write the given side
75 ft
50 ft
lengths.
85 ft
Start
60
ft
Determine the remaining
here
100 ft
75 ft
side lengths.
25 ft Double your answer.
What is the perimeter of the gymnastics
floor?
b) What is the perimeter of the rectangular
Luxio TV screen?
40 ft
255 cm
455 cm
4 × 40
=
.............................................................................
c)
160 ft
What is the perimeter of this Polish
stamp
p valued at 40 ggroshi?
=
.............................................................................
cm
d) What is the perimeter of the upper surface
of this regular hexagonal column of basalt
seen at the Giant’s Causeway in Ireland?
47 mm
7 in.
66 mm
=
.............................................................................
e)
mm
What is the perimeter of the rectangular
ceiling of the Sistine Chapel?
=
.............................................................................
f)
in.
What is the perimeter of the eye of the
pentagonal vortex of hurricane Isabel
(2003)?
40 ft
20 miles
130 ft
=
.............................................................................
page 256
ft
=
.............................................................................
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mi
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.5
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MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Calculating the perimeter of polygons using unit conversions.
Convert all measurements to the same unit. (see skill 26.1, page 245 and skill 26.2, page 246)
Determine and label all side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Add together the side lengths.
A. 20 mm = 20 ÷ 10 cm = 2 cm
P =3×2
= 6 cm
Q. Calculate the perimeter of the
equilateral triangle in centimeters.
2 cm
20 mm
mm to cm: ÷ 10
label all sides
2 cm
2 cm
a)
Calculate the perimeter of the trapezoid
in millimeters.
b) Calculate the perimeter of the
quadrilateral in feet.
78 mm
2 in.
27 mm
39 mm
1 in.
1.5 in.
2 cm
.......................................................................................................................
.......................................................................................................................
P=
P=
=
c)
=
.............................................................................
.............................................................................
d) Calculate the perimeter of the
Calculate the perimeter of the right
triangle in millimeters.
parallelogram in millimeters.
4 cm
9 mm
30 mm
41 mm
5.5 cm
.......................................................................................................................
.......................................................................................................................
P=
P=
=
e)
=
.............................................................................
.............................................................................
Calculate the perimeter of the kite in
millimeters.
f)
Calculate the perimeter of this polygon
in centimeters.
32 mm
20 mm
2 cm
56 mm
3.5 cm
2.5 cm
.......................................................................................................................
.......................................................................................................................
P=
P
=
=
.............................................................................
=
.............................................................................
page 257
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© Math’s Mate Blue/Green Skill Builder 27
Skill 27.6
•
•
Determine and label all side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Add together the side lengths.
Q. Calculate the perimeter of this shape.
A.
=
=
OR
=
=
10 mm
18 mm
38 mm
a)
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MMGreen 1 1 2 2 3 3 4 4
Calculating the perimeter of composite shapes.
10 + 10 + 10 + 10 + 18 + 18 + 38 + 18
40 + 54 + 38
132 mm
(10 × 4) + (18 × 3) + 38
40 + 54 + 38
18 mm
10 mm
18 mm
18 mm
132 mm
38 mm
Calculate the perimeter of this shape.
b) Calculate the perimeter of this shape.
2.5 in.
Start
here
0.5 in.
2 cm
6 cm
1 in.
2.5
+ (0.5 × 7) + (1 × 2)
.......................................................................................................................
= 2.5 + 3.5 + 2
=
=
=
.............................................................................
in.
.............................................................................
c)
.......................................................................................................................
Calculate the perimeter of this shape.
cm
d) Calculate the perimeter of this shape.
2.5 in.
3 cm
1.5 cm
1 in.
0.5 in.
4.5 cm
.......................................................................................................................
.......................................................................................................................
=
=
=
.............................................................................
=
in.
.............................................................................
e)
Calculate the perimeter of this shape.
f)
Calculate the perimeter of this shape.
25 mm
8 mm
cm
13 mm
9 mm
16 mm
7 mm
33 mm
.......................................................................................................................
=
=
.............................................................................
page 258
mm
.......................................................................................................................
=
=
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mm
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.7
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MMGreen 1 1 2 2 3 3 4 4
Calculating an unknown side length when the perimeter of a
polygon is given.
• Add together all the given side lengths.
• Subtract the total from the perimeter to find the unknown side length.
OR
• Use algebra.
Q. The perimeter of this regular pentagon
is 7.5 in. What is the length of a side?
? in.
a)
The perimeter of this right triangle is
80 mm. Find the missing side length.
A. If ? represents the length of a side:
P = 7.5 in.
Guess ? = 1.5
P =5×?
7.5 = 5 × ?
? = 1.5 in.
b) The perimeter of this scalene triangle is
108 mm. Find the missing side length.
? mm
? mm
23 mm
16 mm
34 mm
P = 16 + 34 + ?
38 mm
Guess ? = 30
.......................................................................................................................
80 = 50 + ?
so ? =
.............................................................................
c)
mm
The perimeter of this quadrilateral is
7.5 in. Find the missing side length.
P
=
.......................................................................................................................
=
so ? =
.............................................................................
mm
d) The perimeter of this polygon is 170 mm.
Find the missing side length.
? mm
27 mm
0.5 in.
3.5 in.
1.5 in.
43 mm
33 mm
? in.
P
=
.......................................................................................................................
=
so ? =
.............................................................................
page 259
in.
22 mm
P
=
.......................................................................................................................
=
so ? =
.............................................................................
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mm
© Math’s Mate Blue/Green Skill Builder 27
continues on page 261
Skill 27.8
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Calculating the circumference of circles (1).
Substitute the known values into the formula for the circumference.
Hint: You need the radius which is half the diameter.
Q. Using C = 2πr where π ≈
22
, calculate
7
the circumference of the circle.
A. C = 2πr where d = 42 and r = 21
3
22
Simplify: ÷ 7
=2×
× 21
7
= 44 × 3
= 132 mm
r=
d
2
42 mm
a)
Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
b) Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
20 mm
0.5 in.
C = 2πr = 2 × 3.14 × 0.5
.......................................................................................................................
= 1 × 3.14
=
.............................................................................
c)
in.
22
Using C = 2πr where π ≈
, calculate
7
the circumference of the circle.
r=
d
2
C=
.......................................................................................................................
=
=
.............................................................................
d) Using C = 2πr where π ≈
mm
22
, calculate
7
the circumference of the circle.
14 mm
21 mm
C=
.......................................................................................................................
=
=
.............................................................................
page 260
mm
C=
.......................................................................................................................
=
=
.............................................................................
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mm
© Math’s Mate Blue/Green Skill Builder 27
continued from page 260
Skill 27.8
e)
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MMGreen 1 1 2 2 3 3 4 4
Calculating the circumference of circles (2).
Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
f)
Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
1 in.
40 mm
r=
d
2
C
=
......................................................................................................................
C = 2 × 3.14 × 20 where d = 40 and r = 20
......................................................................................................................
= 40 × 3.14
=
.............................................................................
125.6 mm
g) Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
=
=
.............................................................................
h) Using C = 2πr where π ≈
28 mm
C
=
......................................................................................................................
C
=
......................................................................................................................
=
.............................................................................
i)
mm
22
Using C = 2πr where π ≈
, calculate
7
the circumference of the circle.
=
j)
mm
Using C = 2πr where π ≈ 3.14, calculate
the circumference of the circle.
15 mm
C=
......................................................................................................................
=
.............................................................................
page 261
=
.............................................................................
14 mm
=
22
, calculate
7
the circumference of the circle.
50 mm
=
in.
mm
C=
......................................................................................................................
=
=
.............................................................................
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mm
© Math’s Mate Blue/Green Skill Builder 27
Skill 27.9
•
•
•
Calculating the perimeter of composite shapes by first finding
missing side lengths.
Determine the missing sides by adding or subtracting known sides.
Label all side lengths.
Hint: Sides marked with a dash ( ) are of equal length.
Sides marked with two dashes ( ) are of equal length etc.
Add together the side lengths.
Q. Calculate the perimeter of this shape.
21 mm
4 mm
9 mm
A. 21 + 9 + 9 + 18 + 9 + 9 + 21 + 16 + 4 + 16 + 4 + 4
= 30 + 36 + 30 + 44
= 140 mm
Start
here
21 mm
4 mm
16 mm
9 mm
If left length measures
4 + 16 + 16 = 36 mm
Find unknown then right length measures
side length
9 + 9 + ? = 36 mm
So unknown side = 18 mm
36 mm
16 mm
Find unknown
side length
a)
MMBlue 1 1 2 2 3 3 4 4
MMGreen 1 1 2 2 3 3 4 4
Calculate the perimeter of this shape.
Start
here
21 mm
If opposite side = 21 mm
then unknown side = 21 mm
b) Calculate the perimeter of this shape.
Find unknown
side length
Find unknown
side length
15 mm
6 mm
16 mm
12 mm
10 mm
25 mm
x mm = 16 − 6 − 6 = 4
40 mm
21 + 4 + 15 + 6 + 12 + 6 + 12 + 6 + 6 + 6 + 6 + 16
.......................................................................................................................
.......................................................................................................................
= 40 + 36 + 40
=
=
.............................................................................
=
.............................................................................
c)
mm
Calculate the perimeter of this shape.
mm
d) Calculate the perimeter of this shape.
17 mm
27 mm
13 mm
17 mm
28 mm
.......................................................................................................................
=
=
.............................................................................
page 262
mm
.......................................................................................................................
=
=
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mm
© Math’s Mate Blue/Green Skill Builder 27
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MMGreen 1 1 2 2 3 3 4 4
Skill 27.10 Calculating the perimeter of polygons by using Pythagorean
theorem.
•
•
•
Mark all the information given.
Use Pythagorean formula to deduce any unknown side length.
Add together the side lengths.
A. c 2 = a 2 + b 2 where a = 16 and b = 30
c 2 = 16 2 + 30 2
Pythagorean
c 2 = 256 + 900
30 mm
Theorem
2
c = 1156
1156 = 34 × 34
c = 1156
c = 34
Q. Calculate the perimeter of this
parallelogram.
[Hint: Pythagorean theorem will help.]
30 mm
P = 34 + 50 + 34 + 50
= 168 mm
50 mm
Calculate the perimeter of the rectangle.
[Hint: Pythagorean theorem will help.]
50 mm
b) Calculate the perimeter of this isosceles
triangle.
Pythagorean
Theorem
m
m
39 m
39 m
16 mm
34 mm
16 mm
a)
c
[Hint: Pythagorean theorem will help.]
b
36 mm
36 mm
48 mm
36 mm
15 mm
45 mm
15 mm
36 mm
2
39
= 36 2 + b 2 ⇒ b 2 = 1521 − 1296
......................................................................................................................
......................................................................................................................
2
b......................................................................................................................
= 225 ⇒ b = 225 = 15
......................................................................................................................
P = 36 + 15 + 36 + 15 =
.............................................................................
c)
mm
Calculate the perimeter of this
parallelogram. [Hint: Pythagorean theorem will help.]
P =
=
.............................................................................
mm
d) Calculate the perimeter of this isosceles
triangle.
[Hint: Pythagorean theorem will help.]
15 mm
18 mm
72 mm
24 mm
36 mm
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
P =
=
.............................................................................
page 263
mm
P =
=
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mm
© Math’s Mate Blue/Green Skill Builder 27