Segments \( \overline{CD}\) and \(\overline{AB}\) are parallel. If CD = 2, AB = 5, and [CDP] = 4, find [ABCD].
Since [CDP ] = 4
Then the area is (1/2) CD height = (1/2)(2) height = (1/2) (2) (4) = 4
So the height is 4
And triangles CDP and ABP are similar
So the bases are 5/2 = scale factor
So height of ABP = ( 5/2) height of CDP = (5/2) (4) = 10
So....the whole height of ABCD = 10 + 4 = 14
And ABCD is a trapezoid....so its area =
(1/2) (height) ( sum of bases AB + CD) =
(1/2) ( 14) ( 5 + 2) =
7 * 7 =
49 = [ ABCD ]