Question

a stop sign is in the shape of a regular octagon. each side measures 12.4 inches and the apothem of the octagon measures 15 inches. what is the area of the stop sign? 93 square inches 186 square inches 744 square inches 1,488 square inches

Explanation:

Step1: Calculate the perimeter of the octagon

A regular octagon has 8 sides. Given each side \(s = 12.4\) inches. The perimeter \(P\) of a regular polygon is \(P=ns\) (where \(n\) is the number of sides). So, \(P = 8\times12.4=99.2\) inches.

Step2: Use the formula for the area of a regular polygon

The formula for the area \(A\) of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter. Given \(a = 15\) inches and \(P=99.2\) inches. Then \(A=\frac{1}{2}\times15\times99.2\). First, \(15\times99.2 = 1488\), and then \(\frac{1}{2}\times1488=744\) square inches.

Answer:

744 square inches