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Area of composite shapes

Find the area of composite shapes by splitting them into rectangles, triangles and semicircles.

Worked examples

Area of an L-shaped figure

Straightforward

Problem

An L-shaped figure is formed by taking a 9 m×7 m9 \text{ m} \times 7 \text{ m} rectangle and removing a 3 m×4 m3 \text{ m} \times 4 \text{ m} rectangle from one corner. Find the area.

Area of a shape with a triangle

Moderate

Problem

A composite shape consists of an 8 cm×5 cm8 \text{ cm} \times 5 \text{ cm} rectangle with a triangle of base 8 cm8 \text{ cm} and height 3 cm3 \text{ cm} on top. Find the total area.

Area of a shape with a semicircle

Challenging

Problem

A composite shape is formed by a 12 cm×6 cm12 \text{ cm} \times 6 \text{ cm} rectangle with a semicircle of diameter 6 cm6 \text{ cm} attached to one of the shorter ends. Find the total area to 2 decimal places.

Practise

Q1·Straightforward
An L-shaped figure is formed by taking a 10 m×6 m10 \text{ m} \times 6 \text{ m} rectangle and removing a 4 m×2 m4 \text{ m} \times 2 \text{ m} rectangle from one corner. Find the area in m².
Q2·Straightforward
A composite shape is made of two rectangles joined together. One rectangle measures 7 cm×3 cm7 \text{ cm} \times 3 \text{ cm} and the other measures 4 cm×5 cm4 \text{ cm} \times 5 \text{ cm}. Find the total area in cm².
Q3·Straightforward
An L-shaped figure is formed by taking a 12 cm×5 cm12 \text{ cm} \times 5 \text{ cm} rectangle and removing a 3 cm×4 cm3 \text{ cm} \times 4 \text{ cm} rectangle from one corner. Find the area in cm².
Q4·Straightforward
A step-shaped figure consists of two rectangles. The upper rectangle measures 8 m×2 m8 \text{ m} \times 2 \text{ m} and the lower rectangle measures 5 m×3 m5 \text{ m} \times 3 \text{ m}. Find the total area in m².
Q5·Moderate
A composite shape is formed by a 12 cm×5 cm12 \text{ cm} \times 5 \text{ cm} rectangle with a triangle of base 12 cm12 \text{ cm} and height 4 cm4 \text{ cm} removed from the top edge. Find the remaining area in cm².
Q6·Moderate
A composite shape consists of an 8 m×6 m8 \text{ m} \times 6 \text{ m} rectangle with a triangle of base 4 m4 \text{ m} and height 6 m6 \text{ m} attached to one end. Find the total area in m².
Q7·Moderate
A 9 cm×4 cm9 \text{ cm} \times 4 \text{ cm} rectangle has a right triangle with base 3 cm3 \text{ cm} and height 4 cm4 \text{ cm} removed from one corner. Find the remaining area in cm².
Q8·Moderate
A composite shape is formed by a 10 m×5 m10 \text{ m} \times 5 \text{ m} rectangle with a triangle of base 10 m10 \text{ m} and height 3 m3 \text{ m} placed on top. Find the total area in m².
Q9·Challenging
A composite shape is formed by a 10 cm×6 cm10 \text{ cm} \times 6 \text{ cm} rectangle with a semicircle of diameter 6 cm6 \text{ cm} attached to one of the shorter ends. Find the total area to 2 decimal places in cm².
Q10·Challenging
A square with side length 10 m10 \text{ m} has a semicircle of diameter 10 m10 \text{ m} removed from one side. Find the remaining area to 2 decimal places in m².
Q11·Challenging
A composite shape is formed by an 8 cm×5 cm8 \text{ cm} \times 5 \text{ cm} rectangle with a semicircle of diameter 8 cm8 \text{ cm} attached to one of the longer sides. Find the total area to 2 decimal places in cm².
Q12·Challenging
A stadium-shaped figure is formed by a 6 m×4 m6 \text{ m} \times 4 \text{ m} rectangle with a semicircle of diameter 4 m4 \text{ m} attached to each of the shorter ends. Find the total area to 2 decimal places in m².