So I have this problem where I have to find the ratio between the area of the four gray triangles and the whole parallelogram (AS=SC, AX=XS, CY=YS, XZ=ZS, SW=WY). So I decided since this ratio will be the same as the ratio of ADB and XZD+XZB we can simplify the problem. I also added a middle point of AD and AB and created 2 more triangles. Then I assumed they all have the same area (APX, AXF, FXB, PXD, DXZ, DSZ, BXZ, BSZ) so it has to be 1/4.
But how do I prove they all have the same area? Where do I start?
But how do I prove they all have the same area? Where do I start?
