what is the area of a hexagon with a 48 inch perimeter? i know its 166.277 but i need that in square root form?
I don't think you want it in square root form.
The area is 166.277 square inches.
figure one triangle. Area=1/2 b*h
but each interior angle of the triangle is 60 deg, so b/2h=tan30
then total area=6*area of one triangle.
tan 30=1/sqrt3 if you want it in square root form.
To find the area of a regular hexagon, you need to know the length of one side. However, in this case, we are given the perimeter of the hexagon, which is 48 inches.
To find the length of one side, we divide the perimeter by the number of sides in the hexagon, which is 6:
Length of one side = Perimeter / Number of sides = 48 inches / 6 = 8 inches
Once we have the length of one side, we can use the formula to find the area of a regular hexagon:
Area = (3 * sqrt(3) * side length^2) / 2
Substituting the value of the side length, we have:
Area = (3 * sqrt(3) * 8^2) / 2
= (3 * sqrt(3) * 64) / 2
= 192 * sqrt(3) / 2
= 96 * sqrt(3)
So, the area of the hexagon in square root form is 96 * sqrt(3) square inches.