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 \(A=\frac{1}{2}\times perimeter\times apothem\).

Step2: Substitute the given values into the formula

We are given that the perimeter \(P = 22.45\) cm and the apothem \(a=2.16\) cm.
Substitute these values into the formula: \(A=\frac{1}{2}\times22.45\times2.16\).
First, calculate \(22.45\times2.16 = 22.45\times(2 + 0.16)=22.45\times2+22.45\times0.16=44.9+3.592 = 48.492\).
Then, \(A=\frac{1}{2}\times48.492\).
\(A = 24.246\).

Answer:

\(24.2\space cm^{2}\) (the fourth option)