Geometry

Question Analysis

The main focus of this question is to calculate the perimeter of a regular octagon. First, we must determine the length of one side of the octagon using the distance formula between two given points. Then, we utilize the fact that all sides of a regular octagon are equal to calculate the perimeter. This assesses the understanding of coordinate - geometry concepts and the properties of regular polygons.

 

Key Concept Explanation

Distance Formula: Given two points  and  in a coordinate plane, the distance  between them is .

Regular Octagon: A regular octagon has 8 sides of equal length. The perimeter  of a regular octagon is , where  is the length of one side.

 

Step - by - Step Solution

1. Find the length of one side:

Let  and .

Apply the distance formula:

First, calculate  and :  and

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