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XAT 2023 — QA & DI Question 8

Basics of QuadrilateralsEasy

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC < AD. P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC. If the area of the triangle CPD is 4√3, find the area of the triangle ABQ.

Answer & solution

  • 2√3

  • B

    4√3

  • C

    4

  • D

    4√3

  • E

    None of the above

Solution

Given that, CPD is an equilateral triangle

​​​​​​​

∠CPD = ∠PDC = ∠DCP = 60°

AQ || PC ⇒ ∠CPD = ∠QAP = 60°
BC || AD ⇒ ∠QAP = ∠AQB = 60°

⇒ AQCP is a parallelogram, hence AQ = PC = a

∆AQB is a 30°-60°-90° triangle.
⇒ BQ = 1/2 × AQ = a/2

Comapring âˆ†AQB and âˆ†CPD
Base AQ = 1/2 × PD while the heights of both triangles is same.
⇒ Area of âˆ†AQB = 1/2 × Area of âˆ†CPD = 2√3

Hence, option (a).

XAT 2023 QA & DI Q8: ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC < AD. P is a point — Solution | TheCATExam