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 Find the area (Posted on 2011-02-09)
The diagonals of the trapezoid ABCD intersect at P.
The area of the triangle ABP is 216 and the area of CDP is 150.

What is the area of the trapezoid ABCD?

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 Solution | Comment 1 of 4
`The diagonals of a trapezoid divide itinto four triangles. Two of the triangles( those having a side in common with thelateral  sides of the trapezoid ) haveequal areas. Therefore, AB and CD areparallel.`
`Let [UV...YZ] denote the area of polygonUV...YZ.`
`From the above we have`
`   [BPC] = [DPA]                      (1)`
`For any convex quadrilateral we have`
`   [APB][CPD] = [BPC][DPA]            (2)`
`Combining (1) and (2)`
`   [BPC]^2 = [APB][CPD] = 216*150           = 180^2`
`Therefore,`
`   [ABCD] = [APB] + [BPC] + [CPD] + [DPA]`
`          =  216  +  180  +  150  +  180`
`          =  726`
` `

 Posted by Bractals on 2011-02-09 19:02:24

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