Question

question 9 of 10
to the nearest square unit, what is the area of the regular heptagon shown below?
21.6
20.8
a. 1572 square units
b. 5545 square units
c. 792 square units
d. 2772 square units

Explanation:

Step1: Recall area formula for regular polygon

The area formula for 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 $a = 21.6$ and the length of one side $s=20.8$.

Step2: Calculate the perimeter

A heptagon has $n = 7$ sides. The perimeter $P=ns$. So, $P = 7\times20.8=145.6$.

Step3: Calculate the area

Substitute $a = 21.6$ and $P = 145.6$ into the area formula $A=\frac{1}{2}aP$. We get $A=\frac{1}{2}\times21.6\times145.6$. First, $\frac{1}{2}\times21.6 = 10.8$. Then, $A=10.8\times145.6=1572.48\approx1572$.

Answer:

A. 1572 square units