©TeeJay Publishers
Homework for Level F book
Ch 23 - Areas
Chapter 23
Areas
Calculators may be used in
this Chapter
where appropriate.
Exercise 1
1. Write down the formula for the area of a rectangle.
2. Find the area of each shape below (show formula and working) :–
(a)
(b)
(c)
7 mm
9m
6 cm
20 cm
0·5 mm
11 m
3. Explain how you would find the area of a right angled triangle.
4. Find the area of each right angled triangle below :–
(a)
(b)
(c)
8 mm
8m
11 cm
6·5 mm
11 cm
10 m
5. Calculate the shaded area each time here :–
(a)
(b)
4m
4m
2m
7m
6m
(c)
5m
9m
8m
2·5 m
20 m
this is Chapter Twenty Three
page 41
AREAS
©TeeJay Publishers
Homework for Level F book
Ch 23 - Areas
Exercise 2
1. Write down the formula for the area of any triangle.
2. Use the formula each time to calculate the area of : –
(a)
(b)
(c)
12 m
15 cm
4m
10 m
10 cm
6m
3. Which of the three triangles has the smallest area :–
10 m
A
6m
10 m
B
8m
9m
7m
8m
4. A company logo uses a rectangle
(4 metres by 3 metres) and two
pairs of isosceles triangles, each
with height 1 metre, as shown.
C
1m
4m
3m
Calculate the total area of the logo.
5. Given that all three triangles below have the same area, find the values of a and b.
8m
6m
10 m
a m
12 m
this is Chapter Twenty Three
page 42
bm
AREAS
©TeeJay Publishers
Homework for Level F book
Ch 23 - Areas
Exercise 3
1. Write down the formula for the area of a Rhombus or Kite.
2. Use your formula to calculate the area of each shape.
(a)
(b)
(c)
3·5 cm
10 cm
10 cm
20 cm
5 cm
(d)
12 cm
(e)
25 mm
15 mm
(f)
23 cm
7 cm
10 cm
40 cm
3. Six identical silver rhombi (like the one
shown) are made into a pendant below.
3·6 cm
8 cm
Find the total area of the pendant.
4. Calculate the shaded area of the V-kite shown.
5. A rhombus has the same area as the V-kite in question 4.
70 cm
70 cm
If the rhombus has one diagonal length of 100 centimetres,
find the length of the other diagonal.
this is Chapter Twenty Three
page 43
AREAS
©TeeJay Publishers
Homework for Level F book
Ch 23 - Areas
Exercise 4
1. Write down the formula for the area of a parallelogram.
2. Calculate the area of each parallelogram below :–
(a)
(b)
(c)
5 cm
15 cm
15 cm
6 cm
5 cm
8 cm
3. Three identical parallelograms are put
together as shown.
Find the area of one of the parallelograms.
12 cm
8 cm
4. A large parallelogram has an area of 125 square centimetres.
If the parallelogram has a height of 10 centimetres,
find the length of its base.
5.
An “ARROW” sign is formed from 2
identical parallelograms.
40 cm
Calculate the area of the sign.
25 cm
40 cm
Exercise 5
1. Write down the formula for the area of a trapezium.
2. Use the formula to calculate the area of each trapezium below :–
(a)
10 cm
12 cm
(b)
(c)
10 cm
24 cm
15 cm
16 cm
17 cm
16 cm
this is Chapter Twenty Three
15 cm
page 44
AREAS
©TeeJay Publishers
Homework for Level F book
3. At the Gym Trapezium, a sign has been hung
over the doorway with dimensions shown.
Calculate the area of the sign.
Ch 23 - Areas
1m
G y m
T r a p e z i u m
1m
3·2 m
12 cm
4.
Four identical trapezia are joined together
as shown for a company logo.
Calculate the area of the sign.
40 cm
20 cm
? cm
5. The area of the trapezium shown is 154 cm2.
7 cm
Calculate the length of the missing dimension.
24 cm
Exercise 6
For each shape below, use an appropriate formula and calculate the shaded areas :–
(Show all your formulae and working)
1.
2.
20 cm
6 cm
3.
10 cm
12 cm
12 cm
20 cm
12 cm
4.
2 cm
5.
5 cm
5 cm
20 cm
12 cm
6.
30 cm
10 cm
8·7 cm
10 cm
15 cm
6 cm
8 cm
this is Chapter Twenty Three
page 45
AREAS
©TeeJay Publishers
Homework for Level F book
Ch 23 - Areas
Revision Exercise
1. Calculate the area of each of the following shapes (show all formulae and working) :–
(a)
(b)
(c)
6m
50 mm
10 m
(d)
20 mm
10 m
2m
(e)
8 cm
(f)
30 cm
20 cm
75 cm
100 cm
50 cm
75 cm
(g)
50 cm
(h)
4 cm
(i)
10 cm
25 cm
12 cm
4 cm
80 cm
20 cm
2. Calculate the shaded area of each of the following composite shapes :–
(a)
6m
(b)
7m
3m
5m
4m
5m
4m
3m
2m
9m
3. Calculate the length of the missing dimension in each of the following shapes :–
(a)
(b)
Area = 20 cm2
8 cm
? cm
(c)
Area = 100 m2
?m
10 m
Area = 108 m2
? m
20 m
8m
this is Chapter Twenty Three
page 46
AREAS