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Q.5 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

Q.5 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

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
2 years ago
Dear student

Please find the link attached

https://www.askiitians.com/forums/Algebra/22/20489/area-of-trapezium.htm

Regards
Vikas TU
14149 Points
2 years ago
 

Let h and g are the heights of the triangles AOB and COD respectively.Then, 1/2 x AB x h = p and 1/2 x CD x g = q so, AB = 2p/h and 2q/g also, p/q = AB2/CD2 so, AB/CD = vp/vq

Area of trapezium = 1/2(sum of parallel sides) x distance between them

                        =1/2 (AB + CD) x (h + g)

                        = 1/2 (vp/vqCD + CD) x (2p/AB +2q/CD)

Now replacing AB by 2p x vq/vp x CD and then solving the equation we get the area as (vp +vq)2 .     

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