To find the area of a regular hexagon with a side length of [tex]\(20\)[/tex] meters, we can use the formula for the area of a regular hexagon:
[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \cdot \text{side length}^2 \][/tex]
We can follow these steps to do the calculation:
1. Square the side length of the hexagon:
[tex]\[ \text{side length}^2 = 20^2 = 400 \][/tex]
2. Multiply this by [tex]\( \frac{3 \sqrt{3}}{2} \)[/tex]:
[tex]\[ \text{Area} = \frac{3 \sqrt{3}}{2} \cdot 400 \][/tex]
This can be simplified as:
[tex]\[ \text{Area} = 3 \cdot 200 \cdot \sqrt{3} \][/tex]
Let's multiply the factors:
[tex]\[ \text{Area} = 600 \cdot \sqrt{3} \][/tex]
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:
[tex]\[ \text{Area} = 1039.2304845413264 \][/tex]
Finally, we will round off the area to the nearest tenth:
[tex]\[ \text{Area (rounded)} = 1039.2 \][/tex]
So, the area of the regular hexagon rounded to the nearest tenth is [tex]\( 1039.2 \)[/tex] square meters.
