Problem 8 · 2016 Math Kangaroo
Easy
Geometry & Measurement
area-fractionsymmetry
In rectangle ABCD the side AD is 10 cm long. M and N are the midpoints of sides AB and CD. How large is the grey area?
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Answer: C — 100 cm²
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Hint 1 of 2
The rectangle's width is AD = 10, and AB is twice that, so find the whole area.
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Hint 2 of 2
By the symmetry of the semicircle pattern, the grey region is exactly half of the rectangle.
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Approach: grey is half of the rectangle by symmetry
- AD = 10 cm, and the figure is two squares side by side, so AB = 20 cm and the rectangle area is 20 × 10 = 200 square cm.
- In each square the grey and white regions are congruent halves, so the grey area is half of 200 = 100 square cm.
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