Find the area of the regular hexagon. A=4
The formula to find the area of a regular hexagon is:
Area = (3√3 / 2) * s^2
Given that the area is 4, we can set up the equation as follows:
4 = (3√3 / 2) * s^2
8 = 3√3 * s^2
8 / (3√3) = s^2
(8 / (3√3)) * (√3 / √3) = s^2
(8√3) / 9 = s^2
Now, find the value of s:
s = √((8√3) / 9)
s ≈ 1.63
Finally, calculate the area:
Area = (3√3 / 2) * (1.63^2)
Area ≈ 4.09
Therefore, the area of the regular hexagon is approximately 4.09.
Find the area of the regular hexagon. A=4
Given that the area of the regular hexagon is 4, we can use the formula for the area of a regular hexagon:
Area = (3√3 / 2) * s^2
where s is the length of each side of the regular hexagon.
To find s, we rearrange the formula:
4 = (3√3 / 2) * s^2
s^2 = 4 / (3√3 / 2)
s^2 = 8 / 3√3
s = √(8 / 3√3)
s = √(8) / √(3√3)
s = 2√2 / √(3√3)
s = 2√(2/3)
Now that we have s, we can substitute it back into the formula for the area of a regular hexagon:
Area = (3√3 / 2) * (2√(2/3))^2
Area = (3√3 / 2) * (2^2 * 2/3)
Area = (3√3 / 2) * (8 / 3)
Area = 8√3 / 6
Area = 4√3 / 3
Therefore, the area of the regular hexagon when the area is 4 is approximately 4√3 / 3, or approximately 2.31 units squared.