ABCD is a trapezi

It can be observed that ΔADX and ΔACX lie on the same base AX and are between the same parallels AB and DC.

Area (ΔADX) = Area (ΔACX) (i)

ΔACY and ΔACX lie on the same base AC and are between the same parallels AC and XY

Area (ΔACY) = Area (ACX) (ii)

From equations (i) and (ii), we obtain

Area (ΔADX) = Area (ΔACY)