What is the area of a regular hexagon with a radius of 10.39 and a side measuring 12?

To determine the area of a regular hexagon, we use the formula:

[

\text{Area} = \frac{3\sqrt{3}}{2} s^2

]

where ( s ) is the length of one side of the hexagon. In this case, the side length is given as 12. Plugging this value into the formula gives:

[

\text{Area} = \frac{3\sqrt{3}}{2} (12)^2

]

[

\text{Area} = \frac{3\sqrt{3}}{2} \times 144

]

[

\text{Area} = 216\sqrt{3}

]

To find the numerical value of ( 216\sqrt{3} ), we approximate ( \sqrt{3} ) as about 1.732:

[

216 \times 1.732 \approx 374.04

]

Thus, the calculated area of the regular hexagon is approximately 374.04. This confirms that the correct answer corresponds to option A. It is crucial to note that while the radius of the hexagon was provided, it does not directly affect