From the figure we know that △ APB and parallelogram ABCD lie on the same base AB and between the same parallels AB and DC
So we get
Area of △ APB = ½ (Area of parallelogram ABCD) …….. (1)
In the same way △ BQC and parallelogram ABCD lie on the same base BC and between the same parallels BC and AD
So we get
Area of △ BQC = ½ (Area of parallelogram ABCD) …….. (1)
Using the equations (1) and (2)
We get
Area of △ APB = Area of △ BQC
Therefore, it is proved that Area of △ APB = Area of △ BQC.