Geometry

Question Analysis

The main focus of this question is to calculate the perimeter of a regular hexagon. First, we need to find the length of one side of the hexagon using the distance formula between two given points. Then, we use the property that all sides of a regular hexagon are equal to calculate the perimeter. This tests 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 Hexagon: A regular hexagon has 6 sides of equal length. The perimeter  of a regular hexagon 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 the values inside the square root:

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