A regular octagon has side length 10.9 inches. The perimeter of the octagon is 87.2 in centimeters and the area is 392.4 inches squared. A second octagon has side lengths equal to 21.8 inches. Find the area of the second octagon. Round to the nearest hundredth.

Question

surana · Answer

I just want to make this clear that question above was asked by someone affiliated with me, and is not a question I'm directly asking. It's just that they're asking me to ask it.

rational · Answer

you want to learn this and then planning to teach them ?

surana · Answer

They kind of need help, so I'm intending on learning it and then working it through with them, so basically that.

rational · Answer

Awesome! start by finding the "scale factor"

surana · Answer

Scale factor/

surana · Answer

That's the what one number on the octagon is on the other, right?

rational · Answer

Exactly! you can obtain "scale factor" by taking ratio of corresponding sides

michele_laino · Answer

for example, we have:
scale factor = 21.8/10.9=...?

surana · Answer

I think that's a 2/1 ratio, if I'm correct.

michele_laino · Answer

yes!

surana · Answer

Okay, so as a 2-1 ratio, given what's going on, I just take 392.4 inches and double it, right?

michele_laino · Answer

that's right!

rational · Answer

thats a very good wrong guess, but you're very close!

surana · Answer

Dah. Let me try again...

rational · Answer

first square the "scale factor", then multiply it by 392.4

surana · Answer

Square the scale factor, hang on.

rational · Answer

you're correct about scale factor = 2

surana · Answer

475.24/118.81?

rational · Answer

thats right, but you could have simply squared 2 to get 4

rational · Answer

scale factor = 2

(scale factor)^2 = 4

surana · Answer

I thought you meant to choose the actual numbers so that's what I did.

rational · Answer

Ahh okay i see.. multiply that by 392.4 and you're done

surana · Answer

So 392.4 x 2 is what I have to do?

rational · Answer

392.4 x 4 is what you have to work

surana · Answer

Oh, thank you.

michele_laino · Answer

Sorry I think about perimeters not area! @Surana

rational · Answer

basically all regular octagons are similar,
and the area scales as "square of scale factor" 

so when you're given area of some polygon and asked to find the area of another similar polygon, you may work it by simply multiplying the area by (scale factor)^2

surana · Answer

Okay, thank you. I'll be back in a few moments to see if the person got it.

surana · Answer

And they did, joy. Thanks everyone! Medals all around.

rational · Answer

Sweet :)

michele_laino · Answer

thanks! and sorry again,  for my error! @Surana

surana · Answer

It's alright.