Answer:
314 in² (nearest whole number)
Step-by-step explanation:
<u>Radius of a regular polygon</u>: The distance from the <u>center</u> of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
- radius = 11 in ⇒ side length = 11 in
To find the area of a regular polygon, we first need to calculate the apothem. The <u>apothem</u> is the line drawn from the center of the polygon to the midpoint of one of its sides.
where:
- s = length of one side
- n = number of sides
Given:
- s = 11 in
- n = 6
Substitute the given values into the formula and solve for a:
<u>Area of a Regular Polygon</u>
where:
- n = number of sides
- s = length of one side
- a = apothem
Given:
- n = 6
- s = 11
Substitute the given values into the formula and solve for A: