CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 11 : A trapezium \(\text{ABCD}\) has side \(\text{AD}\) parallel to \(\text{BC}, \angle \text{BAD}=90^{\circ}, \text{BC}=3 \text{~cm}\) and \(\text{AD}=8 \text{~cm}\). If the perimeter of this trapezium is \(36 \text{~cm}\), then its area, in sq. \(\text{cm}\), is

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Video Explanation

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Explanatory Answer

Drawing the diagram from the given information…

8 + h + 3 + DC = 36
h + DC = 25
h, 5, DC form a Pythagorean triplet.
12, 5, 13 works, since 12 + 13 = 25 holds.
Therefore, h = 12
Area = 12 * 3 + \(\frac{1}{2}\) * 12 * 5 = 66 sq. units

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The answer is '66'