different shapes of equal size cake

angelalsmith · #1 $Old$ October 12th, 2009, 03:12 PM

Sally made a cake in an 8inx8in pan, which she wants to share with her friends. She wants to divide the cake with 3 friends. She wants to divide the cake equally among 4 people while giving each person a different shaped piece of cake. She wants one piece to be a triangle, one piece to be a quadrilateral, one piece to be a pentagon, and one piece to be a hexagon. Show how Sally can divide the cake. Explain how you know that each person received the same amount of cake.

pickslides · #2 $Old$ October 12th, 2009, 03:45 PM

Does the entire amount of cake have to be used?

angelalsmith · #3 $Old$ October 12th, 2009, 04:38 PM

yes. the entire cake needs to be used.

Deadstar · #4 $Old$ October 13th, 2009, 12:26 PM

Step 1. Cut cake as in attachment.

Step 2.

Step 3.
Cake smoothies shared out in 4 equal glasses!

They all got different shaped cake bits and they all eventually got equal amounts!

Swlabr · #5 $Old$ October 15th, 2009, 02:38 AM

Quote:

Originally Posted by angelalsmith $View Post$

Sally made a cake in an 8inx8in pan, which she wants to share with her friends. She wants to divide the cake with 3 friends. She wants to divide the cake equally among 4 people while giving each person a different shaped piece of cake. She wants one piece to be a triangle, one piece to be a quadrilateral, one piece to be a pentagon, and one piece to be a hexagon. Show how Sally can divide the cake. Explain how you know that each person received the same amount of cake.

Are we allowed to use the Axiom of Choice?