Question

a regular octagon is shown below. 11 m what is the area of the octagon? round your answer to the nearest tenth. square meters

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 given side length into the formula

Given \(s = 11\) m. Then \(A=2(1 + \sqrt{2})\times11^{2}\)

First, calculate \(11^{2}=121\)

Next, \(1+\sqrt{2}\approx1 + 1.414=2.414\)

Then \(2\times2.414\times121\)

\(2\times2.414 = 4.828\)

\(4.828\times121=4.828\times(120 + 1)=4.828\times120+4.828\times1\)

\(4.828\times120=(4 + 0.828)\times120=4\times120+0.828\times120=480+99.36 = 579.36\)

\(579.36+4.828 = 584.188\)

Answer:

\(584.2\)