Geometry

Question Analysis

The main focus of this question is to calculate the perimeter of a regular decagon. We first need to find the length of one side using the distance formula between two given points in the coordinate plane. Then, we use the property that all sides of a regular decagon are equal to calculate the perimeter. This tests the understanding of coordinate - geometry and regular polygon concepts.

 

Key Concept Explanation

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

Regular Decagon: A regular decagon has 10 sides of equal length. The perimeter of a regular decagon 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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