Calculate the Area of a Hexagon with diameter of 14

To solve this problem, we'll proceed with the following steps:

• Step 1: Interpreting the given measure as the diameter of the hexagon and finding the radius.
• Step 2: Calculate the side length using the radius.
• Step 3: Determine the area using the formula for a regular hexagon.

Here's the detailed process:

Step 1: The given length of 14 is the diameter of the hexagon, which means the diagonal from one vertex, passing through the center, to the opposite vertex. The radius ($r$) from the center to a vertex would be half of this diameter:

$r = \frac{14}{2} = 7$

Step 2: The side length $s$ for a regular hexagon is related to the radius by the central triangle consistency (equilateral triangles formed by connecting the center). The side length is equal to the radius:

$s = r = 7$

Step 3: Now, use the formula for the area of a regular hexagon:

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

Substitute the side length calculated:

$\text{Area} = \frac{3\sqrt{3}}{2} \cdot 7^2$

$\text{Area} = \frac{3\sqrt{3}}{2} \cdot 49$

$\text{Area} = \frac{3\sqrt{3}}{2} \cdot 49 \approx 127.3$

Therefore, the area of the hexagon is approximately $\mathbf{127.3}$. This matches choice 2 in the list of possible answers.