The area of a regular hexagon can be calculated using the formula:
Area = (3√3/2) × r²
Where r is the radius (distance from the center to a vertex) of the hexagon.
In this case, the radius is given as 5 inches. Plugging in the value:
Area = (3√3/2) × 5²
Calculating 5² gives us 25:
Area = (3√3/2) × 25
This simplifies to:
Area = (75√3)/2
If we calculate this numerically, we find:
Area ≈ 64.95
Thus, the area of the regular hexagon with a radius of 5 inches is approximately 64.95 square inches.