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?
The diagonals of a trapezoid divide it
into four triangles. Two of the triangles
( those having a side in common with the
lateral sides of the trapezoid ) have
equal areas. Therefore, AB and CD are
parallel.
Let [UV...YZ] denote the area of polygon
UV...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 20110209 19:02:24 