Question

Find the area of a regular hexagon, rounded to the nearest tenth of an inch. The only measurement I'm given is from the center of the hexagon to one of the corners, which is 15 inches.

Answer 1

Was the other problem we did like this not correct?

Answer 2

@swanson_kaitlin

Answer 3

It was, and I tried to apply how we did that one to this one, but I couldn't figure this one out.

Answer 4

I'll get the diagram ready and then see what we can remember.

Answer 5

The regular hexagon will break into six congruent equilateral triangles. One of those six triangles is shown on the attachment.

Answer 6

@swanson_kaitlin

Question: Have you yet studied about apothems of regular polygons?

Question: Have you studied areas of triangles?

No big deal but your answers will let me know how best to help. Okay?

Answer 7

Yeah, I just learned about apothems of regular polygons and areas of triangles recently, so they're still pretty new to me.

Answer 8

Okay. We'll proceed.

Answer 9

The apothem is the perpendicular distance from the center of the hexagon to one of the sides of the hexagon.

The base of the equilateral triangle is bisected by the apothem. 15/2 = 7.5.

Your task (see attachment) is to solve the shown equation for a. The equation comes from the Pythagorean Theorem.

Post what you get and we'll compare answers. Okay?

Answer 10

I get A squared plus 7.5 squared equals 15 squared. After simplifying all of that I get A squared equals 168.75, but it's a decimal so I can't take the square root, and I don't know how to go on from here.

Answer 11

You can use an online calculator to do square roots so don't despair. Just a sec and let me see what I get.

Answer 12

What you did is correct.
The positive square root is 12.99.
So, that is the apothem.

Now, the Area = 1/2 of 12.99 times 90
(90 is the perimeter of the hexagon --> 6 times 15)

Answer 13

Your Task:

What is this equal to:

Area = 1/2 of 12.99 times 90

@swanson_kaitlin

Answer 14

I got 584.6, which is one of the multiple choice answers. Thank you!

Answer 15

That's what I got. Alrighty, then.