Question

In the adjoining fig. ABCD is a //gram.P is a point on AB and Q on AD. Prove that area(ΔPDC) = area(ΔBQC)

Answer 1

Draw a perpendicular PE from P to CD.  Draw a perpendicular QF from Q to BC.

Area of parallelogram ABCD = base * height
        = AB* PE = CD * PE = BC * QF 

Area of triangle PDC  = 1/2 * base * altitude = 1/2 * PE*CD

Area of triangle BQC = 1/2 * base * height = 1/2 * QF * BC

Each of the two triangle's area = 1/2 * area of parallelogram 
hence they are equal