CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 21 A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm , of the square \(A C E G\) is

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Video Explanation

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Explanatory Answer

Interior angle of a regular octagon \(=\frac{n-2}{n} \times 180^{\circ}\)
\(=\frac{8-2}{8} \times 180^{\circ}=135^{\circ}\)
Area of \(\operatorname{ACEG}=a^2\)
In \(\triangle B A C\), using cosine rule:
\[ \begin{array}{l} c^2=a^2+b^2-2 a b \cos C \\ a^2=6^2+6^2-2(6)(6) \cos 135^{\circ} \\ a^2=72-\left(72 \times \frac{-1}{\sqrt{2}}\right) \\ a^2=36(2+\sqrt{2}) \end{array} \]

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The question is "A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm , of the square \(A C E G\) is"

Hence, the answer is '\(36(2+\sqrt{2})\)'

Choice C is the correct answer.

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