We will first need to find the side length and the perimeter of the polygon. Then we will use the formula A= 12ap to find the area.
Finding the Perimeter
To find the perimeter, we first need the side length of the polygon. Notice that we have a right triangle formed by the radius and the apothem.
The apothem bisects any side length of the polygon. By solving the right triangle, we will have half of the side of the polygon. Let's use the Pythagorean theorem to find the value of l.
Let's take the positive root because l is a distance. Therefore, the value of l is sqrt(5.11). Moreover, the length of one side of the given regular polygon is 2* sqrt(5.11)= 2sqrt(5.11).
In a regular pentagon all five sides have the same length. Therefore, we can obtain its perimeter by multiplying the length of a side by 5.
Perimeter: 2sqrt(5.11)* 5= 10sqrt(5.11)
Finding the Area
Finally, we have that the apothem is 3.3 and that the perimeter is 10sqrt(5.11). To find the area, we will substitute these two values in the formula A= 12ap and simplify.
