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

I don't know how to solve the problem, but I do have the formula to find the Area of a regular polygon.\[A = \left(\begin{matrix}1 \\ 2\end{matrix}\right) aP\]

Answer 2

You can also use \[A=2a^{2} \sqrt{3}\] it's the same but you don't need the perimeter so it's a bit faster..

Answer 3

Is a the apothem?

Answer 4

Yes

Answer 5

Thank you

Answer 6

Since they gave you the length of a side they probably want you to use the perimeter formula though.

Answer 7

Would that be the one I had put?

Answer 8

Yes. 'P' is the perimeter and you can find it using the side length they gave you.

Answer 9

Ok. So how would I find the perimeter with just 1 side length?

Answer 10

You know how long one side is, and you know how many sides there are (it's a hexagon, so 6). So: \[P=6s\]\[P=6*12\]\[P=72\]

Answer 11

Ooh. Cool Thank you for your help.

Answer 12

No problem.

If you need to check your answer, all of the following work:

\[A=\frac{3\sqrt{3}}{2}t^{2}\]\[A=\frac{\sqrt{3}}{2}d^{2}\]\[A=\frac{aP}{2}\]\[A=2a^{2}\sqrt{3}\]

Where:
a= apothem
P= perimeter
t= side length
d= flat-to-flat distance (i.e. twice the apothem)

Answer 13

Wow. I never seen those before. Where do you get them?

Answer 14

3 and 4 are ones I just know. 1 and 2 are out of and old textbook I still have from back when I was in college.

Answer 15

Wow. Do you have a degree in Geometry?

Answer 16

Civil Engineering

Answer 17

What do you in Civil Engineering?