Question

using the image below, find the area. select one: a. 40.8 m² b. 175 m² c. 204.4 m² d. 81.8 m²

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.

Step2: Calculate the perimeter

The polygon is a pentagon with side length $s = 10$m. The perimeter $P$ of a pentagon is $P=5s$. So, $P = 5\times10=50$m.

Step3: Identify the apothem

The apothem $a = 7$m.

Step4: Calculate the area

Substitute $a = 7$m and $P = 50$m into the area formula $A=\frac{1}{2}aP$. We get $A=\frac{1}{2}\times7\times50=175$m².

Answer:

B. 175 m²