Area of Compound Shapes

A compound shape is a shape made by joining two or more simple shapes, such as rectangles, triangles and circles, or by cutting one out of another. An L-shape is two rectangles joined; a wall with a door and a round window cut out is a compound shape too. To find its area, work with the simple shapes inside it.

Split it into simple shapes, find each area, then add them. An L-shape splits into a 5 m by 2 m rectangle, area 10 m², and a 2 m by 1 m rectangle, area 2 m²; the total is 12 m². Work out any missing lengths from the ones given before you start. American sites call these composite shapes.

No. Each simple shape has its own formula: length × width for a rectangle, ½ × base × height for a triangle, π × r² for a circle. In a shape made of a rectangle and a right-angled triangle, the rectangle is 5 × 4 = 20 m² and the triangle ½ × 4 × 3 = 6 m², so the total is 26 m². The only rule is add or subtract.

Add when shapes are joined; subtract when a shape is cut out. A 4 m by 3 m wall has a 2 m by 1 m door and a window of radius 0.5 m: the wall is 12 m², the door 2 m² and the window about 0.79 m², so the painted area is about 9.2 m². At £5 a square metre, about £46.

Yes, a whole circle or part of one. Use π × r² for the circle and halve it for a semicircle, then add or subtract like any other part. A rectangle 8 cm by 6 cm with a semicircle of radius 4 cm on top has area 48 + ½ × π × 4² = 48 + 8π cm², about 73 cm².