The area of the parallelogram ABCD is 12. Point E is the midpoint of side AB. Find the area of the trapezoid EBCD.

Let us denote the sides of the parallelogram ABCD by a and b:

| AB | = | CD | = a;

| BC | = | AD | = b;

and the angle between AB and CD through α.

The parallelogram area will be equal to:

S = a * b * sinα;

Knowing that

| AE | = ½ * | AB | = ½ * a;

for the area of the triangle AED we get:

S1 = ½ * AE * AD * sinα = ½ * (a / 2) * b * sinα;

S1 = ¼ * a * b * sinα = ¼ * S

The area S2 of the EBCD trapezoid is:

S2 = S – S1;

S2 = S – ¼ * S = ¾ * S = ¾ * 12 = 9;

Answer: the area of the trapezoid is 9