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ABCD is a trapezium with AB and CD as parallel sides. The diagonals intersect at O. The area of the triangle ABO is p and that of the triangle CDO is q. Prove that the area of the trapezium is (√p +√q) 2

ABCD is a trapezium with AB and CD as parallel sides. The diagonals intersect
at O. The area of the triangle ABO is p and that of the triangle CDO is q.
Prove that the area of the trapezium is (√p +√q)2 

Grade:10

1 Answers

Vikas TU
14149 Points
7 years ago
Triangle CDO / triangle APO = CD^2/ AB^2
    q/p = CD^2/AB^2
     CD / AB = root q / root p 
then, CD = root q and AB = root p
area 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 )^2

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