Question

An equilateral triangle with side length of 6 is circumscribed about a circle which is circumscribed about a square. Determine the area of the square.

Answer 1

area
$area = {(2r)}^{2}$
=48

Answer 2

Find the radius of the circle:

The  equilateral triangle is inscribed in a circle, therfore the radius of the circle can be be found by (Side/ √3)

Radius = Side / √3

Radius = 6 /√3

Find the length of the square:

Length of the square is the diameter of the circle

Length = 2 x radius

Length = 2 x (6 / √3)

Length = 12 / √3

Find the area of the square:

Area = Length x Length

Area = (12 / √3)² = 144/3 = 48 units²

Answer: The area is 48 units²