Problem 27 · 2012 Math Kangaroo
Stretch
Geometry & Measurement
area
The shape pictured is made out of two squares with side lengths 4 cm and 5 cm respectively, a triangle with area 8 cm² and the grey parallelogram. What is the area of the parallelogram?
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Answer: B — 16 cm²
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Hint 1 of 2
The triangle's two sides are the sides of the squares (4 and 5); use its area to find the angle.
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Hint 2 of 2
The parallelogram has the same two side lengths but the supplementary angle.
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Approach: relate triangle and parallelogram through the shared angle's sine
- The triangle has sides 4 and 5 (shared with the squares); its area ½·4·5·sinθ = 8 gives sinθ = 0.8.
- The grey parallelogram has the same two sides 4 and 5 but the supplementary angle, whose sine is also 0.8.
- So its area is 4·5·0.8 = 16 cm² (B).
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