Question

the base of the right triangle drawn in the regular octagon measures 0.7 cm.
what is the perimeter of the octagon?
○ 11.2 cm
○ 14.1 cm
○ 15.2 cm
○ 20.8 cm

Explanation:

Step1: Recall the property of a regular octagon

A regular octagon has 8 equal - length sides. The right - triangle drawn from the center of the octagon to a side is such that the base of the right - triangle (\(0.7\) cm) is half of the side - length of the octagon.

Step2: Calculate the side - length of the octagon

Let \(s\) be the side - length of the octagon. Then \(s = 2\times0.7=1.4\) cm.

Step3: Calculate the perimeter of the octagon

The formula for the perimeter \(P\) of a regular polygon is \(P = n\times s\), where \(n\) is the number of sides and \(s\) is the side - length. For an octagon, \(n = 8\) and \(s = 1.4\) cm. So \(P=8\times1.4\).

$$P = 11.2$$

Answer:

11.2 cm