Problem 9 · 2022 Math Kangaroo
Medium
Geometry & Measurement
area-fraction
The sides of the square ABCD are 10 cm long. What is the total area of the shaded part?
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Answer: C — 50 cm²
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Hint 1 of 2
Look at how the picture splits into matching shaded and unshaded pieces.
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Hint 2 of 2
By the picture's symmetry the shaded part and the white part are the same size.
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Approach: use symmetry to take half the square
- The square has area 10 × 10 = 100 cm².
- The diagonals split the square into four matching pieces, and the picture shades exactly half of them.
- So the shaded part is half of 100, which is 50 cm².
- So the answer is C.
Mark:
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