Geometry

Question Analysis

The main focus of this question is to find the area of a regular hexagon. It requires applying the formula for the area of a regular polygon, which involves the apothem and the perimeter of the polygon. This tests the understanding of regular polygon area concepts.

Key Concept Explanation

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

Step - by - Step Solution

1. Calculate the perimeter :

For a regular hexagon with side length  meters, and since a hexagon has  sides, the perimeter .

Substitute  and  into the formula:  meters.

2. Calculate the area :

Given the apothem  meters, use the area formula

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