XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 20 : \(A B C D\) is a trapezoid where \(B C\) is parallel to \(A D\) and perpendicular to \(A B\). Kindly note that \(B C \lt A D\). \(P\) is a point on \(A D\) such that \(C P D\) is an equilateral triangle. \(Q\) is a point on \(B C\) such that \(A Q\) is parallel to \(P C\). If the area of the triangle CPD is \(4 \sqrt{3}\), find the area of the triangle ABQ.

Video Explanation

Explanatory Answer

By dropping a perpendicular CR from C to PD, we observe that ΔCRP and ΔABQ are congruent. Area of ΔCRP = \( \frac { 1 } { 2 } \times \triangle C P D = 2 \sqrt { 3 } \)
Area(ΔABQ) = Area(ΔCRP) = \( 2 \sqrt { 3 } \) sq. units.

The answer is '\(2 \sqrt{3}\)'

Choice A is the correct answer.

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