Geometry

Question Analysis

The main focus of this question is to calculate the perimeter of a regular heptagon. We need to first 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 heptagon are equal to find the perimeter. This tests the understanding of coordinate - geometry and the characteristics of regular polygons.

 

Key Concept Explanation

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

Regular Heptagon: A regular heptagon has 7 sides of equal length. The perimeter  of a regular heptagon is calculated as , 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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