Question

determine the area of the regular hexagon.
10 ft
12 ft
a 260 ft squared
b 360 ft squared
c 460 ft squared
d 560 ft squared

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: Identify apothem and side - length

The apothem $a = 10$ ft and the side - length of the hexagon is $s=12$ ft.

Step3: Calculate perimeter of hexagon

A hexagon has 6 sides. So, $p = 6s$. Substituting $s = 12$ ft, we get $p=6\times12=72$ ft.

Step4: Calculate area of hexagon

Substitute $a = 10$ ft and $p = 72$ ft into the area formula $A=\frac{1}{2}ap$. So, $A=\frac{1}{2}\times10\times72 = 360$ ft².

Answer:

B. 360 ft squared