Question

question 10 of 10
to the nearest square unit, what is the area of the regular octagon shown below?
18.1
15
a. 272 square units
b. 543 square units
c. 2172 square units
d. 1086 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 $a = 18.1$ and the side length $s=15$.

Step2: Calculate the perimeter

Since a regular octagon has 8 equal - length sides, the perimeter $P = 8s$. Substituting $s = 15$ into the formula, we get $P=8\times15=120$.

Step3: Calculate the area

Substitute $a = 18.1$ and $P = 120$ into the area formula $A=\frac{1}{2}aP$. So $A=\frac{1}{2}\times18.1\times120=18.1\times60 = 1086$.

Answer:

D. 1086 square units