A regular hexagon has perimeter 60 in. What is the hexagon's area? (1 point) Responses 75in.² 75 Image with alt text: Start Root 3 End Root in.² 150in.² 150 Image with alt text: Start Root 3 End Root in.² 300 in.² 300 Image with alt text: Start Root 3 End Root in.² 600in.²
To find the area of a regular hexagon, we first need to find the length of each side. Since the perimeter is given as 60 inches and there are 6 sides in a hexagon, each side would be 60/6 = 10 inches.
Next, we can use the formula for the area of a regular hexagon:
Area = (3√3 * side length^2)/2
Plugging in the values:
Area = (3√3 * 10^2)/2
Area = (3√3 * 100)/2
Area = 300√3/2
Area = 150√3
Therefore, the area of the regular hexagon is 150√3 in².