ABCD is a quadrilateral and DP//AC.Show that ar(ABP)=ar(ABCD)

Given: ABCD is a quadrilateral and DP//AC.

To Prove: area(ΔABP) = area(quad. ABCD)

Proof: ΔACD  and ΔACP  are on the same base and between the same parallels.

∴ area(ΔACD) = area(ΔACP)

Now, adding area(ΔABC) on both sides, we get,

⇒area(ΔACP)+area(ΔABC) = area(ΔACD)+area(ΔABC)

⇒area(ΔABP) = area(quad. ABCD)