equal areas by 2 straight cuts in a convex quadr. 2021 May Olympiad L1 p4
Source:
August 20, 2021
geometry
Problem Statement
Facundo and Luca have been given a cake that is shaped like the quadrilateral in the figure.
https://cdn.artofproblemsolving.com/attachments/3/2/630286edc1935e1a8dd9e704ed4c813c900381.png
They are going to make two straight cuts on the cake, thus obtaining portions in the shape of a quadrilateral. Then Facundo will be left with two portions that do not share any side, the other two will be for Luca. Show how they can cut the cuts so that both children get the same amount of cake. Justify why cutting in this way achieves the objective.