A regular hexagon and a square are inscribed in a circle, find the area of the square if the side of the hexagon = √ 6.

univerkov | March 4, 2021 | education

Since a regular hexagon is inscribed in a circle, the radius of this circle is equal to the length of the side of this hexagon. ОА = ОВ = R = √6 cm.

The diagonal of a square inscribed in a circle is equal to the diameter of a circle inscribed around it.

MH = D = 2 * R = 2 * √6 cm.

The MCN quadrangle is rectangular and isosceles, then MH2 = 2 * MK2.

MK ^ 2 = MH ^ 2/2 = (2 * √6) 2/2 = 12.

The area of the square is equal to: Sq = MK ^ 2 = 12 cm2.

Answer: The area of the square is 12 cm2.

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