CAT 2024 Slot 3 QA Question 2: A regular octagon ABCDEFGH has sides of length $6$ cm each. Then the area, in sq. cm, of the square ACEG is

Question

A regular octagon ABCDEFGH has sides of length $6$ cm each. Then the area, in sq. cm, of the square ACEG is

Accepted Answer

Let $R$ be the circumradius of the regular octagon. Each side of the octagon is a chord subtending $45^\circ$ at the centre.

$6 = 2R\sin 22.5^\circ$
$6 = R\sqrt{2 - \sqrt{2}}$
$R^2 = \dfrac{36}{2 - \sqrt{2}}$
$R^2 = 18(2 + \sqrt{2})$

The vertices A, C, E and G are alternate vertices of the octagon

A regular octagon ABCDEFGH has sides of length 666 cm each. Then the area, in sq. cm, of the square ACEG is