To find the area of a regular hexagon, we can use the formula:
Area = (3√3 / 2) × r²
where r is the radius of the hexagon.
Given that the radius r is 20, we can substitute this value into the formula:
Area = (3√3 / 2) × (20)²
Calculating it step-by-step, we first find (20)² = 400. Then we substitute:
Area = (3√3 / 2) × 400
Now, let’s calculate:
Area = (1200√3 / 2) = 600√3
To approximate the area, we can use the value of √3 ≈ 1.732:
600 × 1.732 = 1039.2
So, the approximate area of the regular hexagon with a radius of 20 is about 1039.2 square inches.