Question

Geometry 2 Question: Find the area of a regular hexagon. (round to the nearest 10th of an inch.) All I'm given is the measurement from the center to a corner, which is 10in.

Answer 1

Your task is to find the length of side a of the right triangle shown on the diagram. Post what you get and then we'll go to the next step. The right triangle has hypotenuse 10 and one leg of measure 5.

@swanson_kaitlin

Answer 2

For a^2 I got 75, and then I rounded a to 8.7, is that right?

Answer 3

For a, I got 5 times square root of 2 which approximates to 7.071. Let me check my work.

a^2 + 5^2 = 10^2
a^2 + 25 = 100
a^2 = 75
a = sqrt(75) = 5 times square root of 2.

Your work seems correct.

Run square root of 75 through your calculator again. Post what you get.
@swanson_kaitlin

Answer 4

Area of regular hexagon = .5 * a * p where a is the apothem of the hexagon and p is the perimeter.

So, a = 7.071 (subject to your checking)
p = 6 times 10

So, we're ready to complete this:

A = .5 * 7.071 * 60 = ?

Answer 5

I got 212.13, but the 4 possible answers for this question are 255.5 inches squared, 259.8 inches squared, 260.3 inches squared, and 266.7 inches squared.

Answer 6

I got that, too. Look go back to the original question.

You posted: All I'm given is the measurement from the center to a corner, which is 10in.

Corner is not a geometrical term. So, what is the exact wording of the problem? Does your text state "corner?"

Answer 7

Did the question say "center to a side?"

Answer 8

The hexagon in my problem is identical to the one you posted in the diagram.

Answer 9

I think I figured it out, I took the square root of 75, and instead of rounding it to the nearest tenth, I just multiplied the entire thing by 60 on my calculator and divided it by 2 and got 259.8, which is one of the answers. I didn't understand which numbers to multiply to get the area before, so thank you! I think I get it now.

Answer 10

I cranked out 6 times the area of one of the 6 congruent equilateral triangles that comprise the regular hexagon and got 259.8076. So, I think we agree. Let's look at the options.

Answer 11

I am going with this: 259.8 inches squared.
Do you agree? @swanson_kaitlin

Answer 12

Yeah, thank you!

Answer 13

Okay, that's good news.