Thread: hexagon

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

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?

I just would like and explanation please

with this much you should be able to complete

Originally Posted by ibdutt

with this much you should be able to complete

thank you I have solved it to be 4/3

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 $\displaystyle \sqrt{3}/2$. 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: $\displaystyle \left(\frac{1}{\sqrt{3}/2}\right)^2= \frac{1}{3/4}= \frac{4}{3}$.