Question

1. determine the area of the regular hexagon. (round to the hundredths place. numerical value only)

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. The apothem is the distance from the center of the polygon to the mid - point of a side, here $a = 7.79$ m. For a regular hexagon, if the side length $s=9$ m, the perimeter $P = 6s$.

Step2: Calculate the perimeter

Since $s = 9$ m and $P=6s$, then $P=6\times9=54$ m.

Step3: Calculate the area

Substitute $a = 7.79$ m and $P = 54$ m into the area formula $A=\frac{1}{2}aP$. So $A=\frac{1}{2}\times7.79\times54$. First, $7.79\times54 = 410.66$. Then $\frac{1}{2}\times410.66=213.606$ m².

Step4: Round to the hundredths place

Rounding $213.606$ to the hundredths place gives $213.61$ m².

Answer:

$213.61$