Question

Find the area of regular hexagon with point $O$ as its center.

Short answer

The area of regular hexagon is$93.5\text{sq. units}$.

Step-by-step solution

Step 1. Write down the given information.

The given regular hexagon ABCDEF is reconstructed and shown below having given side $BC=6$.

Step 2. Concept used.

A regular hexagon comprises of six equilateral triangles, whose area is given as:

$\text{Area of regular hexagon}=6\left(\frac{\sqrt{3}}{4}{a}^2\right)$, where $\left(a\right)$ is the side of regular hexagon.

Step 3. Calculation.

Evaluating the area of given regular hexagon of given side $BC=6$, by the concept stated above.

$\begin{array}{c}\text{Areaofregularhexagon}=6\left(\frac{\sqrt{3}}{4}{a}^2\right)\\ =\left(6\right)\left(\frac{\sqrt{3}}{4}{\left(6\right)}^2\right)\\ =93.5\text{sq.units}\end{array}$

Hence, the area of regular hexagon is $93.5\text{sq. units}$.

Step 4. Conclusion.

The area of regular hexagon is $93.5\text{sq. units}$.