CAT 2024 Slot 3 QA Q21 Geometry

Question 21 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

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
  1. A
    \(36(1+\sqrt{2})\)
  2. B
    \(72(1+\sqrt{2})\)
  3. C
    \(36(2+\sqrt{2})\)
  4. D
    \(72(2+\sqrt{2})\)

Answer: (C) 36(2+√(2)) Geometry MCQ

Solution

  1. The interior angle of a regular octagon is \(135^\circ\), so in triangle ABC: \(AC^2 = 6^2 + 6^2 - 2 \cdot 36 \cos135^\circ = 72 + 36\sqrt2\).
  2. Square area \(= AC^2 = 36(2 + \sqrt2)\).

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