Question

question 4 of 25
a regular octagon with sides of length 11 and an apothem of length 8.85 has an area of ____ square units.
a. 97.35
b. 430.77
c. 121
d. 778.80
e. 389.40
f. 98.65

Explanation:

Step1: Recall the area formula for a 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 of the octagon

A regular octagon has 8 sides. Given side - length $s = 11$, the perimeter $P=8s$. So, $P = 8\times11=88$.

Step3: Calculate the area of the octagon

We know that $a = 8.85$ and $P = 88$. Substitute these values into the area formula $A=\frac{1}{2}aP$. Then $A=\frac{1}{2}\times8.85\times88$. First, $\frac{1}{2}\times88 = 44$. Then $44\times8.85=389.4$.

Answer:

E. 389.40