Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth.
I apologize for the oversight in my calculations. Thank you for providing the correct formula for finding the area of a regular hexagon.
Using the formula A = 1/2 * ap, where a is the apothem and p is the perimeter, we have:
A = 1/2 * 10.4 * 6 * 12
A = 1/2 * 62.4 * 12
A = 0.5 * 748.8
A = 374.4
Rounded to the nearest tenth, the area of the regular hexagon is approximately 374.4 square yards. Thank you for pointing out the simpler method.
The formula to find the area of a regular hexagon is A = (3√3 x s^2)/2, where s is the length of a side.
Given that the apothem length is 10.4 yards, we can use the formula for the apothem of a regular hexagon, which is apothem = s/2 x √3, to find the length of a side.
10.4 = s/2 x √3
20.8 = s√3
s ≈ 20.8/√3
s ≈ 12 yards
Now we can plug the side length into the formula for the area of a regular hexagon:
A = (3√3 x (12)^2)/2
A = (3√3 x 144)/2
A = (432√3)/2
A = 216√3
A ≈ 374.8
Therefore, the area of the regular hexagon is approximately 374.8 square yards.
what a lot of work! A = 1/2 ap where a is the apothem and p is the perimeter.
A = 1/2 ap = 1/2 * 10 * 6*12 = 50 * 72 = 360