Resque the square

Geometry Level 2

A regular octagon of side length $3 \text{ cm}$ is inscribed in a square. Find the answer if the area of the square is divided by three.

9+6\sqrt 2

3+2\sqrt 3

18

27+2\sqrt 3

1 solution

X X
Aug 18, 2018

Side length of the square= $\dfrac3{\sqrt{2}}+3+\dfrac3{\sqrt{2}}=3+3\sqrt{2}$

Area of the square= $3^2(1+\sqrt{2})^2=3^2(3+2\sqrt{2})$

Divide by 3: $3(3+2\sqrt{2})=9+6\sqrt{2}$