Question

gretchen is refinishing her gazebo that is in the shape of a regular octagon. the length of one side is 3 feet and the apothem is 3.5 feet. what is the area that gretchen will be refinishing? a. 63 sq feet b. 10.5 sq feet c. 42 sq feet d. 24 sq feet

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 and $P$ is the perimeter.

Step2: Calculate the perimeter

A regular octagon has 8 sides. Given side - length $s = 3$ feet, the perimeter $P=8s$. So $P = 8\times3=24$ feet.

Step3: Calculate the area

The apothem $a = 3.5$ feet. Substitute $a = 3.5$ and $P = 24$ into the area formula $A=\frac{1}{2}aP$. Then $A=\frac{1}{2}\times3.5\times24$. First, $\frac{1}{2}\times24 = 12$, and then $12\times3.5=42$ square feet.

Answer:

c. 42 sq feet