Geometry

Question Analysis

The main focus of this question is to calculate the area of a regular decagon. It requires applying the formula for the area of regular polygons, which depends on the apothem and perimeter. 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. Calculate the perimeter :

A decagon 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  and .

First, calculate