Problem 11 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
perimeterspatial-reasoning
A gray square of area 36 cm² and a black square of area 25 cm² are overlaid as shown. What is the perimeter of the overlapping region — the white quadrilateral, which has one vertex on a side of the gray square?
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Answer: B — 11 cm
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Hint 1 of 2
The overlapping white region's sides come from the edges of the two squares.
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Hint 2 of 2
The slanted pieces pair up to recover full side lengths.
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Approach: reassemble the overlap's sides into full square sides
- The white quadrilateral is bounded partly by the gray square's edge and partly by the black square's edge.
- Because a vertex of one square lies on a side of the other, the slanted boundary pieces add up to one full side of each square.
- So the perimeter equals side(gray) + side(black) = 6 + 5 = 11 cm.
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