Geometry

Question Analysis

The main focus of this question is to calculate the perimeter of a regular dodecagon. First, we use the distance formula between two given points to find the length of one side. Then, we rely on the property that all sides of a regular dodecagon are equal to determine the perimeter. It assesses the understanding of coordinate - geometry concepts and the characteristics of regular polygons.

 

Key Concept Explanation

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

Regular Dodecagon: A regular dodecagon has 12 sides of equal length. The perimeter  of a regular dodecagon is , where  is the length of one side.

 

Step - by - Step Solution

1. Find the length of one side:

Let  and .

Calculate  and :

.

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