# The area of the parallelogram ABCD is 56. point E is the midpoint of the CD side. find the area of the trapezoid AECB.

September 14, 2021 | education

| 1. A, B, C, D – the tops of the parallelogram. S – area. h = height.

2.S trapezoid ABED = (DE + AB) / 2 x h.

AB = CD, since the opposite sides of the parallelogram are equal.

DE = 1/2 CD according to the problem statement.

3. Substitute 1/2 CD instead of DE and CD instead of AB into the original expression:

S trapezoid ABED = (CD / 2 + CD) 2 x h = 3SD / 4 x h.

CD x h is the S of the parallelogram. CD x h = 56.

S trapezoid ABED = 56 x 3/4 = 42 units.

Answer: S trapezoid ABED = 42 units.