Question

select the correct answer.
a regular octagon has side lengths of 8 centimeters. what is the approximate area of the octagon?
a. 512 cm²
b. 309 cm²
c. 473 cm²
d. 618 cm²

Explanation:

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

The formula for the area \(A\) of a regular octagon with side length \(s\) is \(A = 2(1+\sqrt{2})s^{2}\).

Step2: Substitute the value of \(s = 8\) into the formula

First, calculate \(s^{2}\): \(s^{2}=8^{2}=64\).
Then, calculate \(1 + \sqrt{2}\approx1+1.414 = 2.414\).
Next, calculate \(2(1+\sqrt{2})\approx2\times2.414 = 4.828\).
Finally, find \(A\approx4.828\times64\).
\(A\approx4.828\times64=(5 - 0.172)\times64=5\times64-0.172\times64=320-11.008 = 308.992\approx309\) \(cm^{2}\).

Answer:

B. \(309\ cm^{2}\)