Find the area of a regular hexagon inscribed in a circle of

Find the area of a regular hexagon inscribed in a circle of radius 8 cm. a) 48 cm2 b) 128 cm2 c) 1923 cm2 d) 963 cm2 e) 1282 cm2

Solution

A regular hexagon, there are 6 equilateral triangles with sides of 8.
The area of each traingle = b*h/2

height = radius*sin60 = 8*sqrt(3)/2

= 4sqrt(3)

So, Area of traingle = 8*(4sqrt(3) )/2 = 16sqrt3

Area of hexagon = 6*area of triangle = 96sqrt(3)

Option d)