Problem 19 · 2025 Math Kangaroo
Hard
Geometry & Measurement
areaarea-fraction
The square shown on the right has sides of 10 cm. The square is divided into two equal-sized rectangles by the vertical centre line. What is the area of the grey section?
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Answer: B — 25 cm²
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Hint 1 of 2
The whole square is 10 × 10 = 100 cm², so try to see the grey as a simple fraction of that whole.
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Hint 2 of 2
The centre lines split the grey ‘bow-tie’ into a left half and a right half; find the area of one half and double it.
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Approach: the grey is two equal triangles meeting at the centre
- The grey shape is a bow-tie: two triangles that meet at the centre of the square, one on the left and one on the right.
- The left triangle has corners at the top-middle of the square, the centre of the square, and the bottom-left corner; counting on a 10×10 grid its area is 12.5 cm², and the right triangle is its mirror image, also 12.5 cm².
- Adding the two halves gives 12.5 + 12.5 = 25 cm², which is exactly one quarter of the 100 cm² square, so the answer is (B) 25 cm².
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