To find the area of a regular 6-sided polygon (hexagon) with a side length of 2 meters, follow these steps:

Formula for the Area of a Regular Hexagon:

The area $A$ of a regular hexagon with side length $s$ can be calculated using the formula: $A = \frac{3 \sqrt{3}}{2} \cdot s^2$

Where:

• $s$ is the length of one side.

Substituting the Given Values:

Given $s = 2$ meters: $A = \frac{3 \sqrt{3}}{2} \cdot (2)^2$ $A = \frac{3 \sqrt{3}}{2} \cdot 4$ $A = 6 \sqrt{3} \, \text{square meters}$

Approximate Value:

We can now compute the approximate value of the area by substituting $\sqrt{3} \approx 1.732$: $A \approx 6 \times 1.732 \approx 10.392 \, \text{square meters}$

Thus, the area of the regular hexagon is approximately $10.39$ square meters.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the formula for the area of a hexagon relate to the area of equilateral triangles?
2. What is the perimeter of the hexagon in this case?
3. How would the area change if the side length was tripled?
4. How does the area formula for a hexagon compare to that for a square or triangle?
5. What other methods can be used to find the area of a regular polygon?

Tip: The formula for a regular polygon's area can be generalized using its apothem and perimeter for more complex shapes.