Question

find the area of a regular hexagon with an apothem of 1.7 cm and a side length of 2 cm. round to the nearest tenth.

Explanation:

Step1: Recall the perimeter formula

For a regular hexagon with side - length $s$, the perimeter $P$ is given by $P = 6s$. Since $s = 2$ cm, then $P=6\times2 = 12$ cm.

Step2: Recall the area formula

The area $A$ of a regular polygon is given by $A=\frac{1}{2}aP$, where $a$ is the apothem and $P$ is the perimeter. Here, $a = 1.7$ cm and $P = 12$ cm. So $A=\frac{1}{2}\times1.7\times12$.

Step3: Calculate the area

$A=\frac{1}{2}\times1.7\times12=1.7\times6 = 10.2$ $cm^{2}$.

Answer:

$10.2$