Area of composite figures
Theory
A composite figure is built from simpler shapes. Split it into rectangles, find each area with \(\text{length} \times \text{width}\), then add them — or surround it and subtract the missing part.
A composite figure is made from simpler shapes joined together. An L-shape, for example, is two rectangles joined at an edge.
To find its area, split it into rectangles with a straight line. Find each area using \(\text{length} \times \text{width}\).
Then add the areas. Because the pieces do not overlap, the parts add up to the whole.
Sometimes it is easier to start with a large rectangle and subtract a missing corner.
There are two ways to reach the same answer.
| Method | What you do |
|---|---|
| Split and add | cut into rectangles, add the areas |
| Surround and subtract | take a big rectangle, subtract the missing part |
How to find the area of a composite figure
- Split the figure into rectangles with a straight line.
- Work out any missing side lengths from the ones you are given.
- Find each area with length times width, then add them.
| \(7 \times 2 + 4 \times 3\) | \(=\) | \(14 + 12\) |
| \(=\) | \(26\,\text{cm}^2\) |
| \(6 \times 2 + 4 \times 2\) | \(=\) | \(12 + 8\) |
| \(=\) | \(20\,\text{cm}^2\) |
| \(9 \times 3 + 5 \times 3\) | \(=\) | \(27 + 15\) |
| \(=\) | \(42\,\text{cm}^2\) |
| \(6 \times 4 - 2 \times 2\) | \(=\) | \(24 - 4\) |
| \(=\) | \(20\,\text{cm}^2\) |
Common pitfalls
Frequently asked questions
What is a composite figure?
A composite figure is a shape made from simpler shapes joined together, such as an L-shape built from two rectangles.
How do you find the area of an L-shape?
Split it into two rectangles, find each area with length times width, then add the two areas together.
How do I find a missing side length?
A missing side is often the difference of two given sides. For example, if the full height is \(5\,\text{cm}\) and part is \(2\,\text{cm}\), the rest is \(3\,\text{cm}\).
Can I subtract instead of adding?
Yes. You can take the area of a large surrounding rectangle and subtract the area of the missing corner. Both methods give the same answer.
Why do the parts add up to the whole?
The pieces do not overlap and cover the whole figure with no gaps, so their areas add up to the total area.