Problem 18 · 2017 Math Kangaroo
Medium
Geometry & Measurement
area-decompositionarea
Two 1 cm long segments are marked on opposite sides of a square with side length 8 cm. The end points of the segments are connected with each other as shown in the diagram. How big is the area of the grey part?
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Answer: B — 4 cm²
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Hint 1 of 2
The two connecting lines cross, forming a bow-tie of two grey triangles.
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Hint 2 of 2
Each grey triangle has a 1 cm base; their heights together span the square.
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Approach: two triangles whose heights sum to the side
- The grey region is two triangles, each with base 1 cm (the marked segments).
- Their apexes meet where the lines cross, and the two heights together span the 8 cm side of the square.
- Total grey area = 1/2 × 1 × 8 = 4 cm².
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