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abcd is trapezium with ab and cd as parallel sides.the diagonals intersect at o. area of triangle abo is p sq.units and that of triangle cdo is q sq. units then area of trapezium is ?

abcd is trapezium with ab and cd as parallel sides.the diagonals intersect at o. area of triangle abo is p sq.units and that of triangle cdo is q sq. units then area of trapezium is ?

Grade:11

1 Answers

Vikas TU
14149 Points
7 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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