Page 174 - Mathematics Coursebook

18.3 Calculating the area and perimeter of compound shapes

18.3 Calculating the area and perimeter of compound shapes

A compound shape is one that is made up of simple shapes such as squares and rectangles.
You work out the area of a compound shape using this method.
1 Split the shape up into squares and/or rectangles.

2 Work out the area of each individual square or rectangle.
3 Add together the individual areas to get the total area.
You work out the perimeter of a compound shape by adding the lengths of all the sides.

Worked example 18.3
5 cm 5 cm
Work out the area and perimeter of this shape.
5 cm
7 cm
8 cm 8 cm A
3 cm B 3 cm

12 cm 12 cm

5 cm 5 cm Start by working out the missing two lengths on the shape.
12 – 5 = 7 cm and 8 – 3 = 5 cm
5 cm Split the shape up into two rectangles and label them A and B.
7 cm Work out the area of rectangle A using area = length × width,
8 cm 8 cm A
Work out the area of rectangle A using area = length × width,
3 cm B 3 cm Work out the area of rectangle B using area = length × width
Work out the area of the compound shape by adding the areas
12 cm 12 cm of the two rectangles. Remember to write the correct units, cm ,
2
Area A = 8 × 5 = 40 cm with your answer.
2
Area B = 7 × 3 = 21 cm Add together all the lengths to get the perimeter.
2
Total area = 40 + 21 = 61 cm Remember to write the correct units, cm, with your answer.
2
Perimeter = 12 + 8 + 5 + 5 + 7 + 3
= 40 cm
) Exercise 18.3

1 a Copy and complete both methods to find the area of this compound shape.
Method 1 Method 2
2 cm 2 cm 2 cm 2 cm

A A

6 cm A 6 cm 6 cm 6 cm
A
B 4 cm B B 4 cm 4 cm B 4 cm

6 cm 6 cm 6 cm 6 cm
Area A = 6 × 2 = Area A = 2 × =
Area B = 4 × = Area B = 6 × 4 =
Total area = + = Total area = + =
b What do you notice about your answers in part a?
18 Area, perimeter and volume 173