what is the area of a hexagon with a base of 11m to the nearest whole number?
You have 6 identical equilateral triangles.
the area of one of them
= (1/2)(11)(11)sin60°
= (121/2)(√3/2)
so the are of the hexagon
= 6(121/2)(√3/2)
=appr 314 to the nearest whole number
To find the area of a hexagon, you can use the formula:
Area = (3√3/2) * s^2
In this formula, "s" represents the length of the side of the hexagon.
Since you know the base of the hexagon is 11m, you need to determine the length of each side.
A hexagon has six equal sides, so to find the length of each side, you divide the perimeter by 6.
The perimeter of a hexagon is calculated by multiplying the length of one side by six:
Perimeter = 11m * 6 = 66m
Since all the sides of a hexagon are equal, each side of this hexagon would be 66m/6 = 11m.
Now you have the length of one side (s = 11m), you can substitute it into the formula to find the area:
Area = (3√3/2) * (11m)^2
Simplifying this calculation:
Area = (3√3/2) * 121m^2
Area = (3 * 1.732/2) * 121m^2
Area = (3.464/2) * 121m^2
Area = 1.732 * 121m^2
Area ≈ 209.912m^2
To the nearest whole number, the area of the hexagon with a base of 11m is approximately 210 square meters.