7-F
Area of composite shapes
KEY CONCEPTS
Composite shapes can be divided into two or more sections, each of which is
a smaller shape with a known area formula. Consider the following examples.
The oval can be
divided into a
rectangle and two
semicircles.
The stop sign can
be broken into a
rectangle and two
trapeziums.
To find the area of a composite shape:
divide it into smaller shapes that have an area formula you know
find the area of each smaller shape
calculate the area of the composite shape by adding (or subtracting) the
areas of the smaller shapes.
Calculate the area of the following shape.
8 cm
6 cm
10 cm
1
The shape can be divided into a rectangle
and a triangle. The height of the triangle is
(8 – 6) = 2 cm.
WRITE
2 cm
8 cm
6 cm
10 cm
2
3
256
Write the formula for the area of a rectangle.
Arectangle = l × w
• Identify the values of the pronumerals.
Substitute these values into the formula and
evaluate.
l = 10 cm; w = 6 cm
Arectangle = 10 × 6
= 60 cm2
• Write the formula for the area of a triangle.
Atriangle = 12 × b × h
• Identify the values of the pronumerals.
Substitute these values into the formula and
evaluate.
b = 10 cm; h = 2 cm
Atriangle = 12 × 10 × 2
= 10 cm2
Add the area of the rectangle and that of the
triangle together to find the total area of the
composite shape. Remember to include the
units with the answer.
Total area = Arectangle + Atriangle
= 60 + 10
= 70 cm2
The area of the composite shape is 70 cm2.
Maths XPRESS 8
Calculate the shaded area in the following diagram:
14 mm
10 mm
24 mm
WRITE
1
The shape can be divided into a circle and a
triangle.
2
• Write the formula for the area of a circle.
Acircle = π r 2
• Find the value of r, the radius of the circle, by
halving its diameter.
D = 24 mm; r = D = 24 = 12 mm
2
2
• Substitute the value of r into the formula and
evaluate.
Acircle = π × 122
= 144π
= 452.39 mm2
• Write the formula for the area of a triangle.
Atriangle = 12 × b × h
• Identify the values of the pronumerals. Substitute
these values into the formula and evaluate.
b = 10 mm; h = 14 mm
Atriangle = 12 × 10 × 14
= 70 mm2
Subtract the area of the triangle from the area of
the circle to find the shaded area. Remember to
include units with the answer.
A = 452.39 – 70
= 382.39 mm2
The shaded area is 382.39 mm2.
3
Even when there is more than one way to divide a composite shape into
smaller shapes, the same answer will always result.
LEARNING EXPERIENCE
Design it!
Equipment: BLM-14 Grid paper
1 Your parents have decided to build a granny flat in the back garden and want you to help with its
design.
The maximum area available is 70 m2. The minimum requirements are a bedroom, a bathroom, a
living room and a kitchen. Depending on the design, you may need to include space for a hallway
and/or a veranda.
Your task is to create the floor plan of the design for the granny flat. You may work in pairs.
The design must include at least three different shapes and must be clearly labelled.
2 Share your design with your classmates.
Chapter 7
Measurement
257