Geometry

Question Analysis

The main focus of this question is to find the perimeter of a regular nonagon. It requires first calculating the length of one side using the distance formula between two points, and then multiplying by the number of sides (9) since all sides of a regular nonagon are equal. This tests the understanding of regular polygon properties and the application of the distance formula.

 

Key Concept Explanation

Distance formula: Given two points and , the distance between them is .

Regular polygon property: In a regular polygon, all sides have equal lengths. So, to find the perimeter of a regular polygon with sides and side length , we use the formula .

 

Step - by - Step Solution

1. Calculate the length of one side:

Let and .

Apply the distance formula:

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