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ABCD is a trapezium with AB and CD as parallel sides. The diagonals intersectat 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

Mahish Kadam , 9 Years ago

Grade 10

1 Answers

Vikas TU

Last Activity: 8 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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