Question

A regular hexagon is inscribed in a circle. If the area of the hexagon is 24root3 cm2 find the area of the circle

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

Join all corners of hexagon with centre of cirlce and u will see 6 equilateral traingles there!!

Let the radius of circle be "r" which is same as side of equilateral traingles!!

Since there are 6 equilateral triangle forming that hexagon!

6×[(root3)/4]a.a=24root3

a=4

Area of circle = πa.a

=16π

=16×3.14

=50.24 cm^2