Free worksheet · Australian Curriculum

Area of composite shapes worksheets with answers

A composite shape is made of simpler shapes joined together or cut out of each other. Learn the two methods, then make a free worksheet with full solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Area of composite shapes, explained

Every composite area question is solved by splitting the shape up or by subtracting a piece. Here's how to choose, with examples.

1. Method 1: split and add

Split the shape into rectangles, triangles or circles, find each area, then add. An L-shape made of an $8$ m by $3$ m rectangle and a $4$ m by $5$ m rectangle has area

$8 \times 3 + 4 \times 5 = 24 + 20 = 44 \text{ m}^2$

2. Method 2: subtract the missing piece

If a piece has been cut out, find the area of the whole shape and subtract the piece. A $12$ cm by $9$ cm rectangle with a $4$ cm by $3$ cm corner removed has area

$12 \times 9 - 4 \times 3 = 108 - 12 = 96 \text{ cm}^2$

3. Rectangles with triangles

A rectangle $10$ m by $6$ m with a triangle on top (base $10$ m, height $4$ m) has area

$10 \times 6 + \frac{1}{2} \times 10 \times 4 = 60 + 20 = 80 \text{ m}^2$

4. Shapes with semicircles

A semicircle is half a circle, so its area is $\frac{1}{2}\pi r^2$ . A rectangle $10$ cm by $6$ cm with a semicircle on a $6$ cm side has $r = 3$ :

$60 + \frac{1}{2} \times \pi \times 3^2 \approx 60 + 14.14 = 74.14 \text{ cm}^2$

Remember to halve the diameter to get the radius.

5. Finding missing lengths

Diagrams often leave a side unlabelled. Use the opposite sides: in an L-shape that is $10$ m wide overall, if the top part is $4$ m wide, the bottom step is $10 - 4 = 6$ m wide. Write every length on the diagram before you calculate.

6. Borders, frames and paths

For a path around a lawn, find the area of the outer rectangle and subtract the lawn. A $12$ m by $8$ m lawn with a $1$ m path all the way around makes an outer rectangle $14$ m by $10$ m:

$14 \times 10 - 12 \times 8 = 140 - 96 = 44 \text{ m}^2$

Add the path width on both sides, not just one.

Quick check: 10 questions

Try each one, then open the answer.

A shape is made from a $5$ cm by $2$ cm rectangle and a $3$ cm by $4$ cm rectangle. Find its area.
Answer
$10 + 12 = 22$ cm²
A $3$ m by $3$ m square is cut out of a $10$ m by $8$ m rectangle. Find the area left.
Answer
$80 - 9 = 71$ m²
A $12$ cm by $5$ cm rectangle has a triangle on top with base $12$ cm and height $4$ cm. Find the total area.
Answer
$60 + 24 = 84$ cm²
A $6$ cm square has a semicircle on one side, with that side as its diameter. Find the total area to 2 decimal places.
Answer
$36 + \frac{1}{2}\pi(3)^2 \approx 50.14$ cm²
An L-shape is a $10$ m by $7$ m rectangle with a $4$ m by $3$ m corner removed. Find its area.
Answer
$70 - 12 = 58$ m²
An $8$ m by $5$ m rectangle has a right-angled triangle attached with shorter sides $3$ m and $5$ m. Find the total area.
Answer
$40 + 7.5 = 47.5$ m²
A photo frame is $20$ cm by $15$ cm on the outside and $16$ cm by $11$ cm on the inside. Find the area of the frame.
Answer
$300 - 176 = 124$ cm²
A circle of radius $2$ cm is cut out of a $14$ cm by $6$ cm rectangle. Find the area left, to 2 decimal places.
Answer
$84 - 4\pi \approx 71.43$ cm²
A house-shaped outline is a $9$ m square with a triangular roof of base $9$ m and height $5$ m. Find its area.
Answer
$81 + 22.5 = 103.5$ m²
A $12$ m by $8$ m lawn has a path $1$ m wide all the way around it. Find the area of the path.
Answer
$140 - 96 = 44$ m²

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetArea and perimeter Year 8 worksheetArea and perimeter Year 8 worksheetCircles

Questions

What is a composite shape?

A composite shape is made from two or more simple shapes, such as rectangles, triangles and semicircles, joined together or with one cut out of another.

How do you find the area of a composite shape?

Either split it into simple shapes and add their areas, or find the area of a larger shape and subtract the part that is missing. Choose whichever needs fewer calculations.

Which year level learns composite area?

Composite areas start in Year 7 with rectangles and triangles, and in Year 8 they include circles and semicircles. They also come up again in Year 9 and 10 surface area problems.

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