To find the area of a regular hexagon, you can use the formula:
Area = (3√3/2) × side²
In this case, the side length is given as 10. Plugging this value into the formula to calculate the area, we get:
Area = (3√3/2) × 10²
Area = (3√3/2) × 100
Area = 150√3
Now, if you need a numerical approximation for better understanding, you can calculate:
Area ≈ 150 × 1.732 (since √3 is approximately 1.732)
Area ≈ 259.81
So, the area of a regular hexagon with a side length of 10 is approximately 259.81 square units. This formula works because a regular hexagon can be divided into 6 equilateral triangles, and using the properties of those triangles allows us to derive the formula simply and effectively.