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​Q24. In the given figure, ABCD is a parallelogram. AB is produced to a point P and DP intersects BC at Q. Prove that area ( APD) = area (quad. BPCD) 
  [Hint : Diagonal divides a || gm into two triangles of equal area 
     area ​​ ABD = area ​ DBC
    Again, area ​ BPD = area ​ BPC (  Triangles on the same base and between the same parallel are equal in area )

Hi, We know that diagonal of a parallelogram divides it into two equal triangleso here take diagonal BDand triangle ABDand BCDso area ABD= areaDBC....1again we know that two triangle BPDand BCP are on same base BPand between same parallel AP and CDso area BPD= areaBCP....2Adding equation 1 and 2 area ABD+area BPD=areaDBC+ areaBCParea of APD = area of quadrilateral BPCD

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