The area of a square inscribed in a circle is 8 cm. Find the area of a regular hexagon inscribed in this circle.

The area of the square is equal to the square of the side, we find the side of the square:

Skv = a ^ 2;

a = √Sq = √8 = 2√2 cm2 – side of the square.

The radius of a circle circumscribed about a square:

R = a / √2 = 2√2 / √2 = 2 cm.

The side of a regular hexagon inscribed in a circle is equal to its radius:

b = R = 2 cm.

The area of a regular hexagon is determined by the formula:

Sш = 3√3 * b ^ 2/2;

Ssh = 3√3 * 2 ^ 2/2 = 3√3 * 4/2 = 6√3 ≈ 10.39 cm2.