Question

an equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. what is the area of the equilateral triangle, rounded to the nearest tenth? 2.7 cm² 4.1 cm² 16.2 cm² 24.2 cm²

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area \(A\) of a regular polygon is \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter.

Step2: Substitute the given values into the formula

We are given that \(a = 2.16\) cm and \(P=22.45\) cm.
Substitute these values into the formula: \(A=\frac{1}{2}\times2.16\times22.45\).
First, calculate \(\frac{1}{2}\times2.16 = 1.08\).
Then, calculate \(1.08\times22.45=24.246\).

Answer:

\(24.2\space cm^{2}\) (rounded to the nearest tenth)