Problem 12 · 2009 Math Kangaroo
Medium
Geometry & Measurement
area-decompositionpythagorean-triple
The quadrilateral on the right has side lengths AB = 11, BC = 7, CD = 9 and DA = 3. The angles at A and C are right angles. What is the area of the quadrilateral?
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Answer: C — 48
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Hint 1 of 2
The two right angles let you split the shape with diagonal BD into two right triangles.
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Hint 2 of 2
Add the areas of right triangle ABD (legs 11 and 3) and right triangle CBD (legs 7 and 9).
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Approach: split into two right triangles
- Draw diagonal BD. Angle A is a right angle, so triangle ABD has legs AB = 11 and AD = 3.
- Its area is ½ × 11 × 3 = 16.5.
- Angle C is a right angle, so triangle CBD has legs BC = 7 and CD = 9, area ½ × 7 × 9 = 31.5.
- Total area = 16.5 + 31.5 = 48 — answer C.
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