Question

a planter is shaped like a regular hexagon. the side lengths are 2 meters and the apothem is sqrt{3} meters. what is the area of the hexagonal planter? enter your answer as a decimal to the nearest hundredth. area = square m²

Explanation:

Step1: Find the perimeter of the hexagon

The formula for the perimeter \(P\) of a regular hexagon with side length \(s\) is \(P = 6s\). Given \(s = 2\) meters, then \(P=6\times2 = 12\) meters.

Step2: Use the formula for the area of a regular polygon

The formula for the area \(A\) of a regular polygon is \(A=\frac{1}{2}Pa\), where \(P\) is the perimeter and \(a\) is the apothem. Substitute \(P = 12\) meters and \(a=\sqrt{3}\) meters into the formula: \(A=\frac{1}{2}\times12\times\sqrt{3}\).
First, \(\frac{1}{2}\times12 = 6\). Then \(A = 6\sqrt{3}\).
Calculate \(6\sqrt{3}\approx6\times1.732=10.392\).

Answer:

\(10.39\)