a regular octagon has a radius of 6 ft and a side length of 4.6 ft. what is the approximate area of the…

Explanation:

Step1: Recall area formula for regular polygon

$A=\frac{1}{2}aP$, where $a$ is the apothem and $P$ is the perimeter.

Step2: Find the apothem

For a regular octagon with radius $r = 6$ ft, using right - triangle properties. The apothem $a=\sqrt{6^{2}-\left(\frac{4.6}{2}\right)^{2}}=\sqrt{36 - 5.29}=\sqrt{30.71}\approx5.54$ ft.

Step3: Calculate the perimeter

The side length $s = 4.6$ ft and for an octagon $P=8s$. So $P = 8\times4.6=36.8$ ft.

Step4: Calculate the area

$A=\frac{1}{2}\times5.54\times36.8 = 5.54\times18.4=101.936\approx101$ ft².

Answer:

101 ft²