Find the area of the regular polygon shown below and choose the appropriate result.
6.16 yd
4yd
To find the area of a regular polygon, we can use the formula:
Area = (Perimeter * apothem) / 2
First, let's calculate the perimeter of the regular polygon. Since it is a hexagon (6 sides), the perimeter will be:
Perimeter = 6.16 yd * 6 = 36.96 yd
Next, we need to find the apothem of the regular polygon. The apothem is the distance from the center of the polygon to the midpoint of one of its sides. For a regular hexagon, the apothem is equal to the radius of the circumscribed circle. Since the radius is given as 4 yd, the apothem will also be 4 yd.
Now, we can plug the values into the formula:
Area = (36.96 yd * 4 yd) / 2
Area = 73.92 yd^2
The area of the regular polygon is 73.92 yd^2.