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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.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
6 months ago

The formula to find the area of a regular hexagon is A = (3āˆš3 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 āˆš3, to find the length of a side.

10.4 = s/2 x āˆš3
20.8 = sāˆš3
s ā‰ˆ 20.8/āˆš3
s ā‰ˆ 12 yards

Now we can plug the side length into the formula for the area of a regular hexagon:

A = (3āˆš3 x (12)^2)/2
A = (3āˆš3 x 144)/2
A = (432āˆš3)/2
A = 216āˆš3
A ā‰ˆ 374.8

Therefore, the area of the regular hexagon is approximately 374.8 square yards.

User Icon for oobleck oobleck answered
6 months ago

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

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
6 months ago

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.