To find the area of a regular hexagon with a side length of \(\(20\)\) meters, we can use the formula for the area of a regular hexagon:
\(\[ \text{Area} = \frac{3 \sqrt{3}}{2} \cdot \text{side length}^2 \]\)
We can follow these steps to do the calculation:
1. Square the side length of the hexagon:
\(\[ \text{side length}^2 = 20^2 = 400 \]\)
2. Multiply this by \(\( \frac{3 \sqrt{3}}{2} \)\):
\(\[ \text{Area} = \frac{3 \sqrt{3}}{2} \cdot 400 \]\)
This can be simplified as:
\(\[ \text{Area} = 3 \cdot 200 \cdot \sqrt{3} \]\)
Let's multiply the factors:
\(\[ \text{Area} = 600 \cdot \sqrt{3} \]\)
Since I don't currently have a calculator at hand, I'm unable to work out the exact number, but when you perform this calculation, you would find the exact area, which is:
\(\[ \text{Area} = 1039.2304845413264 \]\)
Finally, we will round off the area to the nearest tenth:
\(\[ \text{Area (rounded)} = 1039.2 \]\)
So, the area of the regular hexagon rounded to the nearest tenth is \(\( 1039.2 \)\) square meters.
