Area of compound shapes
Objective. Split compound rectilinear shapes into familiar parts.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A compound shape is made up of two or more simpler shapes joined together, and its area is found by splitting it into familiar parts such as rectangles and triangles. Once split, calculate the area of each separate part using the appropriate formula, then add all the parts together to find the total area. Sometimes it is easier to find the area of a larger surrounding shape and subtract the area of a missing piece, rather than adding separate parts. Carefully labelling each split section with its own dimensions avoids confusion when combining the results.
Worked example
A compound shape is an L-shape made from a 10 cm by 6 cm rectangle with a 4 cm by 3 cm rectangle removed from one corner. Find the area of the compound shape.
- 1Find the area of the large rectangle: 10×6=60 cm².
- 2Find the area of the removed rectangle: 4×3=12 cm².
- 3Subtract the removed area from the large rectangle: 60−12=48.
- 4State the final compound area.
Answer: 48 cm²
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes forget to work out missing side lengths before splitting a compound shape, leaving a section's dimensions unknown. Always use the given measurements to calculate any missing lengths first.
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