A quadrilateral ABCD has sides AB = 5 units, BC = 12 units, CD = DA and ∠ABC = ∠ADC = 90°. What is the area of the quadrilateral (in square units)?

Question

Accepted Answer

72.25. Using Pythagoras, AC = √(5²+12²) = 13. In △ADC with ∠ADC=90° and AD=DC=a: 2a²=169 → a=13/√2. Area = (1/2×5×12) + (1/2×13/√2×13/√2) = 30 + 169/4 = 30 + 42.25 = 72.25 sq units.

A quadrilateral ABCD has sides AB = 5 units, BC = 12 units, CD = DA and ∠ABC = ∠ADC = 90°. What is the area of the quadrilateral (in square units)?

Explanation

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