Problem 13 · 2021 Math Kangaroo
Medium
Geometry & Measurement
area-decompositiongrid
The area of the large square is 16 cm² and the area of each small (corner) square is 1 cm². What is the total area of the central flower, in cm²?
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Answer: C — 4
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Hint 1 of 2
The big square is 4×4 since its area is 16, and it is split into a 4×4 grid of unit squares.
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Hint 2 of 2
Find the flower's area by combining its petal pieces using the symmetry of the figure.
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Approach: decompose the unit-grid square
- Area 16 means the big square is 4 by 4, so the unit corner squares have side 1 and the centre is the middle of the grid.
- The flower has 8 yellow petals; the 4 'straight' petals each reach from the centre to a side, and the 4 'diagonal' petals reach toward the corner unit squares.
- By symmetry the 8 petals together tile half of the inner 2×2 region around the centre plus matching slivers, and the pieces total 4 cm².
- So the answer is C.
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