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
