Answer:
The Area of the regular polygon=65.35 inches²
Step-by-step explanation:
We are given:
Length of side of polygon = 10 inches
Apothem = 13.07
We need to find area of the regular polygon.
The formula used is: [tex]Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\[/tex]
[tex]Perimeter = Sum \ of \ length \ of \ all \ sides[/tex]
The polygon has 8 sides. so,
[tex]Perimeter = 10+10+10+10+10+10+10+10\\Perimeter = 80[/tex]
Now, finding area of Polygon
[tex]Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (13.07) \times(10)\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (130.7)\\Area \of \ the \ regular \ polygon=65.35 \ inches^2[/tex]
So, the Area of the regular polygon=65.35 inches²
