Find the area of the regular hexagon.A=4

7 answers

For a regular hexagon, the formula to find the area is:

Area = (3√3/2) * s^2

Where s is the side length of the hexagon.

Given that A = 4, we can set it equal to the formula:

4 = (3√3/2) * s^2

Now, we can solve for s:

s^2 = (4 * 2) / (3√3)
s^2 = 8 / 3√3
s^2 = (8/3) * (√3/3)

So, the side length of the hexagon is s = sqrt((8/3) * (1/3√3))

To find the area, we substitute this value back into the formula for the area of a regular hexagon:

Area = (3√3/2) * (8/3) * (1/3√3)

Area = 8/2 = 4

Therefore, the area of the regular hexagon is 4 square units.
Find the area of the regular hexagon.A=4
If the area of the regular hexagon is given as 4 square units, it typically means that the area is a known value and you need to calculate the side length of the hexagon.

For a regular hexagon, the formula to find the area is:

Area = (3√3/2) * s^2

Where s is the side length of the hexagon.

Given that the area is 4 square units, we can set it equal to the formula:

4 = (3√3/2) * s^2

Now, we can solve for s:

s^2 = (4 * 2) / (3√3)
s^2 = 8 / 3√3

So, the side length of the hexagon is s = √(8 / 3√3)

However, simplifying further:

s = √(8) / √(3√3)
s = 2√2 / √(3√3)
s = √(4)√(2) / √(3√3)
s = 2√(2) / √(3)√(3)√(3)
s = 2√2 / 3√3

Therefore, the side length of the regular hexagon is 2√2 / 3√3.

If you need to find the numerical value of the side length or further simplify it, please let me know.
Find the area of the regular hexagon.
A=4
Given that the area of the regular hexagon is 4 square units, we can find the side length of the hexagon and then calculate the area.

For a regular hexagon, the formula for the area is:

Area = (3√3/2) * s^2

Where s is the side length of the hexagon.

Given that the area is 4 square units, we can set this area equal to the formula:

4 = (3√3/2) * s^2

Now, we solve for s:

s^2 = (4 * 2) / (3√3)
s^2 = 8 / 3√3

To simplify the value of s, we can rationalize the denominator:

s^2 = 8 / 3√3 * (3√3 / 3√3)
s^2 = 24√3 / 9 * (√(3)√(3))
s^2 = (8√3) / 3

Thus, the side length of the regular hexagon is s = √((8√3) / 3) units.

To find the area, we substitute this value of s back into the formula for the area of a regular hexagon:

Area = (3√3/2) * ((8√3) / 3)^2
Area = (3√3/2) * (64*3) / 9
Area = (3√3/2) * 192 / 9
Area = 3√3 * 64 / 9 * 2
Area = 192√3 / 18
Area = 32√3 / 3 square units

Therefore, the area of the regular hexagon is 32√3 / 3 square units.
Find the area of the regular hexagon.
A=4

__ units
Given the area of the regular hexagon is 4 square units, and using the formula for the area of a regular hexagon:

Area = (3√3/2) * s^2

Where s is the side length of the hexagon.

We can plug in the given area A = 4 into the formula:

4 = (3√3/2) * s^2

Now, we solve for the side length s:

s^2 = 4 / ((3√3) / 2)
s^2 = 8 / 3√3
s^2 = 8√3 / 9

To find the area, we substitute the side length back into the formula:

Area = (3√3/2) * (8√3 / 9)^2
Area = (3√3/2) * (64*3) / 81
Area = (3√3/2) * 192 / 81
Area = 288√3 / 162
Area = 144√3 / 81
Area = 16√3 / 9 square units

Therefore, the area of the regular hexagon given that A=4 is 16√3 / 9 square units.