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 area formula for regular polygon

The area formula for a regular polygon is $A=\frac{1}{2}ap$, where $a$ is the apothem and $p$ is the perimeter.

Step2: Substitute given values

We are given $a = 2.16$ cm and $p=22.45$ cm. So $A=\frac{1}{2}\times2.16\times22.45$.
First, calculate $\frac{1}{2}\times2.16 = 1.08$.
Then, $A=1.08\times22.45=24.246$ $cm^{2}$.

Step3: Round to nearest tenth

Rounding $24.246$ to the nearest tenth gives $24.2$ $cm^{2}$.

Answer:

$24.2$ $cm^{2}$