Find the area of a hexagon with an apothem of 5.5 times the square root of 3.
A hexagon has six sides, so n=6.
Use the formula given in:
http://www.jiskha.com/display.cgi?id=1336457737
To find the area of a hexagon, you can use the formula:
Area = (3 * sqrt(3) * apothem^2) / 2
Given that the apothem is 5.5 times the square root of 3, let's substitute this value into the formula:
Area = (3 * sqrt(3) * (5.5 * sqrt(3))^2) / 2
First, simplify the expression inside the parentheses:
Area = (3 * sqrt(3) * 5.5^2 * sqrt(3)^2) / 2
Next, simplify the square terms:
Area = (3 * sqrt(3) * 30.25 * 3) / 2
Now, multiply 30.25 and 3:
Area = (3 * sqrt(3) * 90.75) / 2
Finally, simplify the expression:
Area = (3 * sqrt(3) * 90.75) / 2
Area = 272.25 * sqrt(3) square units
Therefore, the area of the hexagon with an apothem of 5.5 times the square root of 3 is 272.25 times the square root of 3 square units.
To find the area of a hexagon, we can use the formula:
Area = (3 * (√3) * a^2) / 2,
where "a" is the length of the apothem.
In this case, the apothem is given as 5.5√3, so we can substitute this value into the formula:
Area = (3 * (√3) * (5.5√3)^2) / 2.
First, let's simplify (5.5√3)^2:
(5.5√3)^2 = (5.5)^2 * (√3)^2 = 30.25 * 3 = 90.75.
Plugging this value into the formula, we get:
Area = (3 * (√3) * 90.75) / 2.
Now, let's calculate the area:
Area = (3 * (√3) * 90.75) / 2 = (3 * (√3) * 90.75) / 2 ≈ 469.768.
Therefore, the area of the hexagon with an apothem of 5.5√3 is approximately 469.768 square units.