Geometry

Question Analysis

The main focus of this question is to calculate the area of a regular polygon. It requires applying the formula for the area of regular polygons, which involves using the apothem and perimeter of the polygon. This tests understanding of geometric concepts related to regular polygon areas.

 

Key Concept Explanation

The formula for the area  of a regular polygon is , where  is the apothem (the perpendicular distance from the center of the polygon to the mid - point of a side) and  is the perimeter of the polygon. For an sided regular polygon with side length , the perimeter .

 

Step - by - Step Solution

1. Identify the number of sides and side length:

This is a heptagon, so . The side length  m.

2. Calculate the perimeter :

Using the formula , we substitute  and . So,  m.

3. Identify the apothem:

The apothem  m.

4. Calculate the area :

Using the formula