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)?
A.72.25✓ Correct
B.72.75
C.74.25
D.74.75
Explanation
Using Pythagoras, AC = √(5²+12²) = 13. In triangle ADC with ∠ADC=90° and AD=DC=a, 2a²=169, so a=13/√2. Area = (1/2×5×12) + (1/2×13/√2×13/√2) = 30 + 169/4 = 30 + 42.25 = 72.25 sq units.
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