Problem 22 · 2009 Math Kangaroo
Stretch
Geometry & Measurement
area-decomposition
ABCD is a square with side length 10 cm. The distance from N to M is 6 cm. Every part that is not shaded grey is either a square or an isosceles triangle. What is the grey shaded area?
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Answer: C — 48 cm²
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Hint 1 of 2
The corner cut-offs and the centred segment NM = 6 fix the small white pieces.
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Hint 2 of 2
Find the total white area (corner squares plus isosceles triangles) and subtract from 100.
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Approach: whole minus white pieces
- The square ABCD has area 10 × 10 = 100.
- The unshaded parts are small squares at the corners and isosceles triangles, fixed by NM = 6 and the side 10.
- Their areas total 52.
- So the grey area = 100 − 52 = 48 cm² — answer C.
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