Question

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.

Answer 1

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

Answer 2

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.

Answer 3

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.