Parallelograms and composite areas
Rearrange or split shapes to calculate areas without double-counting.
Before you begin
- Rectangle and triangle areas
- Adding and subtracting measurements
Rearrange a parallelogram into a rectangle
Cut a triangular piece from one end of a parallelogram and translate it to the other end. The pieces form a rectangle with the original base and perpendicular height. No area is created or lost, so A = bh. As with triangles, the sloping side is not automatically the height. A trapezium can be split into a rectangle and triangles, or paired with a copy to derive its area formula.
Partition a compound shape
For a shape made from simpler parts, draw non-overlapping rectangles or triangles and add their areas. Alternatively, enclose it in a rectangle and subtract the missing parts. Label unknown lengths using the full dimensions minus known parts. State which method you used, keep units consistent, and check that the final area is smaller than any containing rectangle when a piece is missing.
Worked example
A garden is an 8 m by 6 m rectangle with a 3 m by 2 m rectangular corner removed. Find its area.
Show the worked solution
- The full rectangle has area 8 × 6 = 48 m².
- The removed corner has area 3 × 2 = 6 m².
- Subtract the removed area: 48 − 6 = 42 m².
42 m².
Try it yourself
A parallelogram has base 10 cm, sloping side 6 cm and perpendicular height 4 cm. What is its area?
Common mistakes
- Split a shape without gaps or overlapping regions.
- Distinguish perpendicular height from a sloping side.
What can you explain now?
A trapezium has parallel sides 6 cm and 10 cm and perpendicular height 3 cm. Find its area by pairing two identical copies.
Compare with the explanation
24 cm².
The two copies form a parallelogram with base 6 + 10 = 16 and height 3, area 48 cm². One copy has half that area, 24 cm².
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗