Question

For a regular hexagon with apothem $5m$, the side length is about $5.77m$. The area of the regular hexagon is (in $m^2$).

• A. $75.5$
• B. $85.5$
• C. $76.5$
• D. $86.5$

Answer 1

Answer: (D)

$86.5$

For a regular hexagon with apothem $5m$ the side length is about $5.77m$.
Use the formula
$A=\frac{1}{2}pa$
to find the area of the hexagon.
The perimeter of the hexagon is about $6\left(5.77\right)$ or $34.62m$.
Now substitute the values.
$A=\frac{1}{2}\left(34.62\right)\left(5\right)$
Simplify.
$A=\frac{1}{2}\left(173.1\right)$
= $86.5$
$A=\frac{1}{2}\left(173.1\right)$
= $86.5$
Therefore, the area of the regular hexagon is about $86.5m^2$.