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Q)ABCD is a trapezium. AB and CD are parallel sides. Diagonals intersect at a point O.
If the area of the triangle CDO =q and Area of triangle ABO=p
Prove that area of trapezium =(root of p root of q) whole square


Triangle CDO / triangle APO = CD square / AB square
    q/p = CD sq / AB sq
     CD / AB = root q / root p 
then, CD = root q and AB = root p
ar. of triangle ABO = 1/2bh
                        p  = 1/2 root p.h
                         2p/root p = h
                       now, h = 2 root p
   similarly, in triangle CDO 
                                   = 2 root q
                now, ar. of trapezium ABCD = 1/2h(a+b)
                                                          = 1/2(2 root p + 2 root q)( root p + root q)
                                                         = (root p + root q )square
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