Question

A regular hexagon has an area of 516 square. Find the measure of each side if its apothem is 16 meters long. Submit your answer in decimal form form to the nearest hundredth.

Answer 1

To find the measure of each side of a regular hexagon given its area and apothem, we can use the formula for the area of a regular polygon:

\[
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
\]

For a regular hexagon, the perimeter can be expressed in terms of the side length \( s \):

\[
\text{Perimeter} = 6s
\]

Substituting this into the area formula gives:

\[
\text{Area} = \frac{1}{2} \times (6s) \times \text{Apothem}
\]
\[
\text{Area} = 3s \times \text{Apothem}
\]

Given that the area is \( 516 \) square meters and the apothem is \( 16 \) meters, we can substitute these values into the equation:

\[
516 = 3s \times 16
\]

Now solve for \( s \):

\[
516 = 48s
\]

Dividing both sides by \( 48 \):

\[
s = \frac{516}{48}
\]
\[
s = 10.75
\]

Thus, the measure of each side of the regular hexagon is \( \boxed{10.75} \) meters.