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akposevictor

Answer:

Side length = 5.8 in

Perimeter = 29

Area = 58 in²

Step-by-step explanation:

✔️Find Side length using trigonometric ratio:

Angle at center of a pentagon is always 36° (we have measure of a full circle, 360, divided by 10 smaller triangles = 36°)

So:

Reference angle = 36°

Adjacent side = 4 in.

Opp = ½ of the side length of the polygon = x (let's represent this as x)

Thus, apply TOA:

Tan 36 = Opp/Adj

Tan 36 = x/4

4*Tan 36 = x

x ≈ 2.9 in (nearest tenth)

Side length = 2*x = 2*2.9 = 5.8 in

✔️Perimeter = 5*side length

Perimeter = 5*5.8 = 29 in

✔️Area = ½aP

Where,

a = 4 in

P = 29

Plug in the values

A = ½*4*29

A = 58 in²

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