Most shapes are not a rectangle, triangle or trapezoid. But almost any polygon can be cut into those shapes, or seen as one of them with a piece missing.
Key idea
To find the area of a composite polygon, split it into rectangles and triangles and add their areas, or start with a bigger shape and subtract the part that is missing.
Why it works
Area counts unit squares. Cutting a shape into pieces does not create or remove any squares, so the pieces' areas add up to the whole. Taking a piece away removes exactly that piece's squares, which is why subtracting works too.
Worked example: Add the pieces
Find the area of the L-shaped floor in the picture.
- Left rectangle: 6 m by 8 m, so $6 \times 8 = 48$.
- Right rectangle: $11 - 6 = 5$ m by 3 m, so $5 \times 3 = 15$.
- Add: $48 + 15 = 63$.
Answer: 63 square meters
Worked example: Subtract the missing piece
Find the same area by subtracting.
- The full rectangle would be 11 by 8: 88.
- The missing corner is 5 by 5: 25.
- $88 - 25 = 63$. Same answer.
Answer: 63 square meters
Worked example: A rectangle and a triangle
A house shape is a 6 by 5 rectangle with a triangle on top, base 6 and height 3. Find its area.
- Rectangle: $6 \times 5 = 30$.
- Triangle: $\frac{1}{2} \times 6 \times 3 = 9$.
- Total: $30 + 9 = 39$.
Answer: 39 square units
Common mistake
Two things go wrong: using a side length that is not given directly (it often has to be found, like $11 - 6 = 5$), and counting an overlap twice. Quick check: work it out two ways, adding and subtracting. Both should give the same area.