Segments CD and AB are parallel. If CD = 2, AB = 4, and [CDP] = 5, find [ABCD].
+128406 Triangles CPD and APB are similar
The scale factor between these is (4/2) = 2
So....the area of triangle APB = [ CPD] * 2^2 = 5 * 2^2 = 20
Next...the height of triangle CDP can be found as
5 =(1/2) 2 * h
h = 5
So....the height of triangle APB is twice this = 10
So.....the total height of the figure = 5 + 10 = 15
And the area of triangle CPB = area of triangle CDB - area of triangle CPD =
(1/2) (CD) * height of figure - [ CPD] = (1/2)(2)(15) - 5 = 10
And [CPB ] = [ DPA]
So.....the total area of the figure = [ CPB] + [ APB ] + [ CPB ] + [ DPA] =
5 + 20 + 10 + 10 =
45 = [ABCD ]
