Question

question 6 of 25
a regular octagon with sides of length 7 and an apothem of length 10.49 has
an area of ____ square units.

a. 293.72

b. 587.44

c. 73.43

d. 92.39

e. 440.16

f. 79.25

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area \( A \) of a regular polygon is \( A=\frac{1}{2} \times \text{perimeter} \times \text{apothem} \).

Step2: Calculate the perimeter of the regular octagon

A regular octagon has 8 sides, each of length 7. So the perimeter \( P = 8\times7=56 \).

Step3: Substitute the values into the area formula

We know the apothem \( a = 10.49 \) and the perimeter \( P = 56 \). Substituting into the formula \( A=\frac{1}{2}\times P\times a \), we get \( A=\frac{1}{2}\times56\times10.49 \).
First, calculate \( \frac{1}{2}\times56 = 28 \). Then, multiply \( 28\times10.49 = 293.72 \).

Answer:

A. 293.72