Question

Ratio of areas of square and hexagon both inscribed in a circle

Answer 1

When a square or a regular hexagon is inscribed, diagonal of square or hexagon is equal to diameter.

hence area of square = 1/2 x 2r x 2r =2r^2 (Because area of quadrilateral is 1/2 d1 d2)

area of hexagon = 6 x √3/4 r^2 =3√3/2 r^2

You can now divide and find the ratio.