Segments CD and AB are parallel. If CD = 2, AB = 4, and [CDP] = 5, find [ABCD].
Because CD is parallel to AB, ∠DCP=∠CAB because alternate interior angles are congruent. Similarly, ∠CDP=∠DBA. This means that triangle CDP and triangle BPA are similar by the AA postulate. Since we know the area and the base of triangle CDP, we can calculate the height by saying area=base*height/2. 5=2*height/2. Thus, the height is 5. These two triangles have a scale factor of 2/4. Therefore, we can find the height of the second triangle by proportions. 5/x=2/4. By cross multiplying, we get x=10. To find the height of the whole entire trapezoid, we add the height of the first triangle with the height of the second triangle. 5+10=15. Next, by using the area of trapezoids formula A=h(a+b)/2, we get 15(6)/2=45.