Question

a regular hexagon is inscribed in a circle with a radius of 8 ft. find the area of the shaded region shown. give the exact answer.

Answer 1

I have attached the missing image of the hexagon.

Answer:

Area of Shaded region = 34.785 ft²

Explanation:

The area of the circle can be found using the radius given as 8 ft

A_c = πr²

A_c = π(8²)

A_c = 64π ft²

Now, this hexagon can be divided into 6 equilateral triangles with sides of length 8ft and angles of

60°

The trigonometry area rule can be used because 2 sides and the included angle are known. Thus,

Area of hexagon;

A_h = 6 x ½ x 8 x 8 x sin 60

A_h = 166.276878 ft²

Shaded region = area of circle - area hexagon

Shaded region = 64π - 166.276878

Shaded region = 34.785 ft²