If in the following figure (not to scale), ∠DAB + ∠CBA = 90o, BC = AD, AB = 20 cm, CD = 10 cm then the area of the quadrilateral ABCD is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 75 cm2
Triangle BEA & DEC is a right-angled triangle where the right angle is at E.
In triangle DEC,
⇒ x2 + z2 = 100cm
In triangle BEA,
⇒ y2 + (x + y + z)2 = 400
⇒ 2y2 + 100 + 2(xy + yz +zx) = 400
⇒ y2 + xy + yz + zx = 150cm
Area of ABCD = Sum of Area of 2 right triangles
⇒ (1 / 2) × z × x + (1 / 2) × y × (x + y + z)
⇒ (1 / 2) × (y2 + xy + yz + zx) = 150 / 2 = 75cm2