Question

Can anyone help? So confused!!

a hexagonal tray of vegetables has an area of 450 cm^2. What is the length of each side of the hexagon? Also, what is the area at the bottom in terms of the side length?

Answer 1

Split the hexagon into 6 equilaterals. The area of each triangle is then 1/2xbasexheight. The base is what you are trying to find. And height is, using pythagoras, \[\sqrt{(b^2)-(1/2b)^2}\]Expand that to get \[\sqrt{b^2-1/4 b^2}\]Which is the same as \[\sqrt{3/4 b^2}\]or\[\frac{ \sqrt{3} }{ 2 } b\]Then multiply that by b and half it to get the area of each triangle. So that gives you\[\frac{ \sqrt{3} }{ 4 } b^2\]Then multiply that by 6 as there are 6 triangles to get \[\frac{ 6\sqrt{3} }{ 4 } b^2\]or\[\frac{ 3\sqrt{3} }{ 2 } b^2\]Then that is equal to 450 so multiply 450 by 2 to get 900 then divide by 3 to get 300 then divide by root 3 to get 173.2. Then root it to get b which is 13.2 cm.

Answer 2

Does that not make sense? It is hard to visualise.

Answer 3

it kinda does