Problem 8 · 2011 Math Kangaroo
Medium
Geometry & Measurement
areaarea-decomposition
Determine the area of the quadrilateral PQRS shown on the right, where \(PS=RS\), \(\angle PSR=\angle PQR=90^{\circ}\), \(ST\perp PQ\), and \(ST=5\).
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Answer: C — 25
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Hint 1 of 2
Drop the perpendicular ST and notice the two right angles let you rearrange the pieces.
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Hint 2 of 2
Triangles PST and the rest reassemble into a square of side 5.
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Approach: reassemble into a square of side ST
- With PS = RS, ∠PSR = ∠PQR = 90° and ST ⊥ PQ, the quadrilateral cuts and rearranges around ST.
- The pieces form a square whose side equals ST = 5.
- Area = 5² = 25.
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