Geometry

Question Analysis

The main focus of this question is to determine the area of a regular pentagon. It requires the application of the formula for the area of regular polygons, which involves the apothem and perimeter of the polygon. This tests the 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. Calculate the perimeter :

A pentagon has  sides. Given the side length  meters.

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

2. Calculate the area :

Given the apothem  meters.

Using the area formula , we substitute