Question

A regular hexagon is inscribed in a circle. If the area of the hexagon is 24root3 cm2 find the area of the circle.(find the area of segments using area of segment formula.)

Answer 1

$\huge{\pink{answer}}$

Dividing a hexagon into 6 equal parts gives 6 triangles with angle at center being 360/6 = 60 degrees.
Area of hexagon = 6 x area of each triangle
Area of triangle = 1/2 ab Sinβ (where β = angle between the sides)
'a' and 'b' are both = 'r' = the radius of the circle

Area of hexagon = 6 x 1/2 x r x r x Sin 60 = 24√3
                                                             r² = 16
                                                             r = 4 cm

Area of circle = 22/7 x 4² = 50.29 cm²

$\huge{\pink{I hope it helps you}}$