Composite area
How to find the area of a composite shape
A composite figure is made from familiar shapes joined together. For an L-shape, draw one straight cut to create two non-overlapping rectangles, find each area, then add the results.
Grades 4–6 · worked example · 3 practice checks
01
Recognize the problem first
- Look for a concave corner where a straight cut can complete two rectangles.
- Use subtraction to work out any unlabelled length before calculating area.
- The two rectangles may touch along an edge, but their interiors must not overlap.
02
Work through one complete example
Question
An 8 cm by 6 cm rectangle has a 3 cm by 2 cm corner removed. Find the remaining area.
- The upper rectangle is 8 − 3 = 5 cm wide and 2 cm high, so its area is 5 × 2 = 10 cm².
- The lower rectangle is 8 cm wide and 6 − 2 = 4 cm high, so its area is 8 × 4 = 32 cm².
- Add the two non-overlapping parts: 10 + 32 = 42 cm².
AnswerThe L-shape has area 42 cm².
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03
Common mistakes to catch
- Adding the removed corner instead of subtracting it.
- Using perimeter lengths in an area calculation.
- Splitting into overlapping rectangles and counting the shared region twice.
0401 02 03
Try three quick checks
A 10 cm × 7 cm rectangle loses a 4 cm × 2 cm corner. Find the remaining area.
Show answer
62 cm²Two non-overlapping rectangles have areas 24 cm² and 15 cm². Find the composite area.
Show answer
39 cm²A 9 m × 8 m rectangle loses a 3 m × 5 m corner.