# Math Help - hexagon

1. ## hexagon

hi can someone please explain the solution to me please, thanks

2. ## Re: hexagon

Do you want us to find and explain the solution? Or just explain the solution without giving the solution? Where has your working taken you so far?

3. ## Re: hexagon

I just would like and explanation please

4. ## Re: hexagon

with this much you should be able to complete

5. ## Re: hexagon

Originally Posted by ibdutt
with this much you should be able to complete
thank you I have solved it to be 4/3

6. ## Re: hexagon

Good! I presume that you realized from idbutt's picture that the if we take the distance from the center to a vertex of the outer hexagon to be 1, then the distance from the center to the middle of a side of that hexagon is $\sqrt{3}/2$. And that is where the circle touches the hexagon so is a vertex of the inner hexagon. Since those are "equivalent" distances, the ratio of the areas is the square of the ratio of those distances: $\left(\frac{1}{\sqrt{3}/2}\right)^2= \frac{1}{3/4}= \frac{4}{3}$.