Greedy Garisht is celebrating his birthday with 6 of his friends. His mother baked him a birthday cake in the shape of a regular hexagon. Wanting to keep most of the cake, he makes cuts linking the midpoints of every 2 adjacent sides, and distributes these 6 slices to his friends. What proportion of the cake does he have left for himself?

• Answer is 3/4 :)
  area of hexagon = 3*sqrt3*(a^2)/2
  where a is side of cake before cutting
  let x be side of cake after cutting which forms a smaller hexagon of side x
  using cosine rule, side of isosceles triangle formed of x, a/2, a/2,
  x=sqrt3*a/2
  Area of new hexagon,
  3*sqrt3*((sqrt3*a/2)^2)/2
  A2/A1 = 3/4 :)
• 9 years agoHelpfull: Yes(1) No(0)
• had again hexagon type cake
• 9 years agoHelpfull: Yes(0) No(1)