MathDB

4

Part of 2006 May Olympiad

Problems(2)

find area of a triangle created by diagonals of a trapezoid

Source: May Olympiad (Olimpiada de Mayo) 2006 L2

9/12/2018
Let ABCDABCD be a trapezoid of bases ABAB and CDCD . Let OO be the intersection point of the diagonals ACAC and BDBD. If the area of the triangle ABCABC is 150150 and the area of the triangle ACDACD is 120120, calculate the area of the triangle BCOBCO.
geometrytrapezoidareas
colored prism 6x5x5 into 150 cubes 1x1x1

Source: XII May Olympiad (Olimpiada de Mayo) 2006 L1 P4

9/22/2022
With 150150 white cubes of 1×1×11 \times 1 \times 1 a prism of 6×5×56 \times 5 \times 5 is assembled, its six faces are painted blue and then the prism is disassembled. Lucrecia must build a new prism, without holes, exclusively using cubes that have at least one blue face and so that the faces of Lucrecia's prism are all completely blue. Give the dimensions of the prism with the largest volume that Lucrecia can assemble.
3D geometrycombinatoricsColoring