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 10 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

Given \(a = 2.16\) cm and \(p=22.45\) cm.
Substitute into \(A=\frac{1}{2}\times a\times p\), so \(A=\frac{1}{2}\times2.16\times22.45\).
First, calculate \(2.16\times22.45 = 48.492\).
Then, \(A=\frac{48.492}{2}=24.246\).

Answer:

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