Question

Geometry~
This problem totally stumped me on my math quiz today @.@
There is a regular octagon, O1, with an area of 96, and a similar octagon, O2, with sides 5 times the sides of the length of O1's. Find the area of O2.
Thanks! :D

Answer 1

oh would you divide 96 by 8, (because an octagon has 8 sides) then do 8*5 and then multiply that by 8?

Answer 2

I was typing that out when I realized it said area, not perimeter, so that wouldn't work.

Answer 3

yea, but dont you do length times width to find area?

Answer 4

Not for an octagon. You need to find the area of one of the triangles within and multiply that by 8.

Answer 5

so you multiply all the sides together to find the are, which with the first octagon its 96/8. then because the sides on the second one are 5 times the length of the first one, you multiply whatever 96/8 is by 5 and then you multiply all of those together to find the area?

Answer 6

The area of an octagon is \[A=2(1+\sqrt{2})s^{2}\] If we increase the side length from s to 5s we then have \[A=2(1+\sqrt{2})(5s)^{2}\]\[A=2(1+\sqrt{2})25s^{2}\]\[A=50(1+\sqrt{2})s^{2}\] Which gives us \[A_2=25A_1=25(96)=2400\]

You will notice that 25 is just the square of the scale factor. This is because we are dealing with a shape in 2-dimensions so we have to apply the scale factor twice (i.e.x-scale is 5 and y-scale is 5, 5*(5=25). If it was a cube or other 3D shape we would use the cube of the scale factor.

Answer 7

We haven't even learned that in class... we were just told the similar polygons and their areas... T_T

Answer 8

You could also do it by figuring out the side length of the one you know the size of then multiplying by five and using that answer as a side length to find the larger area.

Answer 9

Oh ok, I sort of get it xD thanks!

Answer 10

To do that you would solve for s \[s=\sqrt{\frac{A}{2(1+\sqrt{2})}}\] then go \[s \times 5\] and sub back into the area formula.

It works but it's slow and the square roots get messy.

Answer 11

Ah ok I get it now :D thanks!