an equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. what is the area of…

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

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

Answer

Explanation:

Step1: Recall area - perimeter - apothem formula

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 given values

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, $A=1.08\times22.45$. $1.08\times22.45=(1 + 0.08)\times22.45=1\times22.45+0.08\times22.45$. $0.08\times22.45 = 1.796$ and $1\times22.45 = 22.45$. $A=22.45+1.796=24.246\approx24.2$ $cm^{2}$.

Answer:

$24.2$ $cm^{2}$