Triangle area 12. DE-middle line parallel to side AB. Find the area of the trapezoid ABDE.

Let us write down the condition briefly: Sabc = 12, AB – base, DE || AB.
According to Thales’s theorem, the middle line bisects the sides and the height h.
Then the height of the resulting trapezoids is h / 2.
Then the area of the triangle Sabc = 1/2 * h * AB
Thus, the area of the trapezoid is: Sabde = 1/2 * h / 2 * (DE + AB) = 1/2 * h / 2 * (AB / 2 + AB) = (1/2 * h * AB) * 1/2 * (1/2 + 1) = Sabc * 3/4 = 12 * 3/4 = 9.
Answer: the area of the trapezoid is 6.