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ΔCPD and ||gm ABCD are on the same base CD and between two parallel lines AB and CD.

Therefore, area of ΔCPD = area of ||gm ABCD

But area of ||gm ABCD = area of ΔCPD + area of ΔADP + area of ΔBCP ⇒area of ||gm ABCD = 1/2 area of ||gm ABCD + area of ΔADP + area of ΔBCP ⇒1/2 area of ||gm ABCD = area of ΔADP + area of ΔBCP

In llgm ABCD and triangle DPC lie on the same base DC and between same parallel's AB and DC so area(DPC) = 1/2 area(ABCD) ABCD - DPC = 1/2 area(ABCD) area(ADP) + area(PCB) = 1/2 area(ABCD)

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