STRAND: Measurement
TOPIC:
Area, volume & capacity
Area and perimeter of
composite figures
Composite figures are figures made up of a number of distinct shapes.
Area of a composite figure = sum of the areas of each individual shape
Perimeter of a composite figure = length around the outside edge of the composite figure
WORKED Example 1
Calculate a the area and b the perimeter of
the following shape.
16 cm
WORKED Example 2
Calculate a the area and b the perimeter of the
following shape. State your answers correct to 2
decimal places.
10 cm
12 cm
30 m
15 m
24 cm
48 m
Solution
Solution
The composite shape is made up of a rectangle
and a triangle.
a Area = area of rectangle + area of triangle
Area = length × width + 1--2- × base × height
For the rectangle:
Length = 16 cm, width = 12 cm
For the triangle:
Base = 12 cm (same as width of rectangle),
Height = (24 − 16) = 8 cm
So area = 16 × 12 + 1--2- × 12 × 8
So area = 192 + 48
So area = 240 cm2
The composite shape is made up of a semicircle and a
trapezium.
a Area = area of semicircle + area of trapezium
Area = 1--2- π r 2 + 1--2- (a + b)h
For the semi circle:
r = 1--2- × 30 = 15 mm
For the trapezium:
a = 30 mm, b = 48 mm and h = 15 mm.
b Perimeter = sum of the lengths of 5 sides
Perimeter = 16 + 10 + 10 + 16 + 12
Perimeter = 64 cm
b Perimeter = 1--2- (circumference of circle) +
So area =
1
--2
× π × 152 +
1
--2
× (30 + 48) × 15
So area = 353.43 + 585
So area = 938.43 mm2
Perimeter = 3 side lengths of trapezium
To find missing side length of trapezium:
Let c = hypotenuse of right-angled triangle with
side lengths of 15 and 18
c2 = 152 + 182 (Using Pythagoras’ theorem)
= 225 + 324
= 549
c = 549
c = 23.43
So perimeter = 1--2- × 2π r + 15 + 48 + 23.43
So perimeter = π × 15 + 86.43
So perimeter = 47.12 + 86.43
So perimeter = 133.55 mm
 John Wiley & Sons Australia, Ltd 2001
STRAND: Measurement
TOPIC:
Area, volume & capacity
SKILLBUILDER: Area and perimeter
of composite figures
Try these
Calculate a the area and b the perimeter of each of the following shapes. State your answers correct to 2 decimal places where
appropriate.
1
2
18 m
10 cm
13 m
6 cm
10 m
18 cm
30 m
20 cm
3
4
35 cm
23 cm
7m
49 cm
9m
12 m
5
6
3 mm
5 cm
7 cm
3 mm
5 mm
3 mm
3 mm
15 mm
 John Wiley & Sons Australia, Ltd 2001