Question

calculate the area of the regular polygon. > enter the answer in the space provided. use numbers instead of words. square meters

Explanation:

Step1: Recall area formula for regular polygon

The formula for the area of a regular polygon is $A=\frac{1}{2}aP$, where $a$ is the apothem (the distance from the center of the polygon to the mid - point of a side) and $P$ is the perimeter. Here, the apothem $a = 27.6$ m and the side length $s=40$ m.

Step2: Calculate the perimeter

For a regular pentagon (5 - sided polygon), the perimeter $P=ns$, where $n = 5$ (number of sides) and $s = 40$ m. So $P=5\times40=200$ m.

Step3: Calculate the area

Substitute $a = 27.6$ m and $P = 200$ m into the area formula $A=\frac{1}{2}aP$. We get $A=\frac{1}{2}\times27.6\times200$. First, $\frac{1}{2}\times200 = 100$, then $100\times27.6=2760$ $m^{2}$.

Answer:

2760