How do you find the area of a regular hexagon with a 6-inch radius?

To find the area of a regular hexagon, you can use the formula:

Area = (3√3 / 2) × r²

where r is the radius of the hexagon. In this case, the radius is 6 inches.

Now, let’s calculate it step by step:

1. First, square the radius: 6² = 36.
2. Next, plug this value into the formula:

Area = (3√3 / 2) × 36

3. Now, multiply:

Area = (3√3 / 2) × 36 = 54√3

4. Finally, if you want a numerical approximation, you can calculate:

54√3 ≈ 93.53 square inches.

So, the area of the regular hexagon with a radius of 6 inches is approximately 93.53 square inches.