Question

Find the area of the regular polygon below. leave your answer in simplest radical form.

Answer 1

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

     1/2 x perimeter x apothem

Perimeter = the sum of the lengths of all the sides

Suppose length of one side = x

Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3

Since the polygon have 6 sides so

perimeter = 6x

x = 2(8√3)/√3

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

1/2 x 96 x 8√3

384√3 in²

Answer 2

Answer:

= 384√3 In²

Step-by-step explanation:

The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;

θ = 360/6

 = 60°

Therefore; we can calculate the length of each side;

Tan θ = opp/Adj

Tan θ = x /8√3

 Tan 30 = x /8√3

Therefore; 1/√3 =x /8√3

x = 8√3× 1/√3

   = 8

The length of each side is 8 × 2 = 16 In

The area of the polygon will be;

Area of one triangle multiplied by the number of a triangle;

= 1/2 × 16 × 8√3 ×6

= 384√3 In²