Sheet № 101 · Foundation + Higher · AQA · Edexcel · OCR
Area of Compound Shapes –
Compound shape questions combine two or more simple shapes and ask you to find the total area. These questions appear on both Foundation and Higher papers and test whether you can break a complex figure into parts you already know how to handle. They are worth 3-4 marks and reward clear, well-organised working.
§Key definitions
Question:
An L-shaped room has overall dimensions 10 m by 8 m. A 4 m by 3 m rectangle is missing from one corner. Find the area of the room.
Answer:
69.9 cm² (1 d.p.)
Q1 (Foundation):
A T-shape is formed by a rectangle 10 cm by 3 cm on top of a rectangle 4 cm by 7 cm. Find the total area.
Q2 (Foundation):
An L-shape has overall dimensions 9 m by 7 m with a 5 m by 3 m rectangle removed from one corner. Find the area.
Q3 (Higher):
A shape is made from a rectangle 20 cm by 10 cm with a semicircle of diameter 10 cm added to one end. Find the total area to 1 decimal place.
§Formulas to memorise
Total area = sum of individual areas (when shapes are added together)
Total area = area of whole shape minus area of cut-out (when a piece is removed)
Full rectangle area = 10 × 8 = 80 m²
Missing rectangle area = 4 × 3 = 12 m²
L-shape area = 80 − 12 = 68
Rectangle area = 14 × 6 = 84 cm²
Semicircle radius = 6 ÷ 2 = 3 cm
Semicircle area = ½ × pi × 3² = ½ × pi × 9 = 4.5pi = 14.137...
Shaded area = 84 − 14.137... = 69.862...
Rectangle area = 12 × 5 = 60 cm²
Worked example
An L-shaped room has overall dimensions 10 m by 8 m. A 4 m by 3 m rectangle is missing from one corner. Find the area of the room.
Working: Full rectangle area = 10 × 8 = 80 m² Missing rectangle area = 4 × 3 = 12 m² L-shape area = 80 − 12 = 68
⚠ Common mistakes
- ✗Missing a section. When splitting a shape, make sure every part is accounted for. Label each section and tick them off as you calculate.
- ✗Adding when you should subtract. If a piece is cut out of a larger shape, you must subtract its area — not add it. Read the question for words like "removed" or "shaded".
- ✗Using the wrong dimensions for each part. After splitting the shape, re-read the measurements carefully. A common error is using the overall length when a sub-shape only covers part of it.
- ✗Forgetting to use the correct formula for each sub-shape. Each part of the compound shape may require a different area formula — rectangle, triangle, trapezium, or circle.
✦ Exam tips
- →Sketch the split on the diagram — draw a dashed line to show how you have divided the shape. This helps you and the examiner follow your method.
- →If the shape has a curved part (semicircle, quarter circle), calculate the curved area separately and keep full precision until the final rounding step.
- →Show each sub-area in your working before adding or subtracting. This earns method marks even if the final arithmetic is wrong.
- →Check your answer is reasonable by comparing it to a simple rectangle that encloses the whole shape — your compound area should be smaller than that rectangle.