Area of the overlap?

A hard-level "Area" problem."Add them up, then subtract the excess." Almost every overlap problem yields to this.

GivenSquare with side 10 cm / π = 3.14

Hints

1. Getting the red part directly is hard, so we take a detour. These two dots are the centres of the arcs.
2. First shade only the quarter circle centred on the bottom-left dot. Its area is 10 × 10 × 3.14 ÷ 4 = 78.5 cm².
3. The quarter circle centred on the top-right dot is exactly the same size, 78.5 cm². Together they cover the square with no gaps.
4. Adding them gives 78.5 + 78.5 = 157 cm². But the red part in the middle is covered twice, so it has been counted twice.
5. The square itself is 10 × 10 = 100 cm² — the size when everything is counted once.
6. 157 counts it twice, 100 counts it once. The difference is exactly the red part that was counted again. 157 − 100

Answer 57cm²

More "Area" problems

• Area of the inner triangle?
• Area of triangle DOA?
• Area of quadrilateral ABCD?
• Area of the overlap?
• Total area of the two crescents?
• Area swept by the square?

Browse by idea

• Add, then subtract — an overlap is a counting problem
• Circles and sectors — multiply by π once, at the very end

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