ABCDEF is a regular hexagon. If the perimeter = 12 find the area of ABCDEF.
think of the hexagon as six equilateral triangles. I assume that you can find the area of such a triangle of side 2 (1/6 the perimeter of the hexagon).
Now multiply that area by 6, for the six triangles.
To find the area of a regular hexagon, we need to use the formula:
Area = (3√3/2) * s^2
where "s" is the length of one side of the hexagon.
In this case, we are given the perimeter of the hexagon, which is 12. Since a hexagon has six equal sides, we can divide the perimeter by 6 to find the length of one side.
s = Perimeter / 6
s = 12 / 6
s = 2
Now, we can substitute the value of "s" into the area formula:
Area = (3√3/2) * s^2
Area = (3√3/2) * 2^2
Area = (3√3/2) * 4
Area = 6√3
Therefore, the area of the hexagon is 6√3.