Problem 13 · 2015 Math Kangaroo
Medium
Geometry & Measurement
area-decomposition
The diagram consists of three squares each of side length 1. The midpoint of the topmost square is exactly above the common side of the two other squares. What is the area of the section coloured grey?
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Answer: C — 1
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Hint 1 of 2
Use the side-1 squares as units and locate the grey triangle's base and height.
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Hint 2 of 2
The midpoint of the top square sits above the shared side; use that to get the triangle's dimensions, then area = base times height over 2.
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Approach: compute the grey triangle's area on the unit grid
- Two unit squares sit side by side, with the third unit square centred above their common side.
- The grey region is the triangle cut off by the diagonal across the stacked squares.
- Its base and height give area = 1 square unit.
- So the grey area is 1 (C).
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