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grin007 [14]
3 years ago
14

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

Mathematics
2 answers:
Licemer1 [7]3 years ago
6 0

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

<h3>      1/2 x perimeter x apothem</h3>

<em>Perimeter = the sum of the lengths of all the sides </em>

<em>Suppose length of one side = x</em>

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

<em />

Since the polygon have 6 sides so

perimeter = 6x

<h3>x = 2(8√3)/√3</h3>

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

<h3>1/2 x 96 x 8√3</h3>

384√3 in²

tamaranim1 [39]3 years ago
3 0

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

<h3><u>= 384√3 In²</u></h3>
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