ABCD – parallelogram. Point E – midpoint of DC. S triangle ABC = 65cm3. Find S of triangle ADE + S of triangle BCE.

Since the diagonal of the AC parallelogram divides it into two equal triangles, the area of the parallelogram is equal to: Savsd = 2 * Savs = 2 * 65 = 130 cm2.

Let’s draw a straight line EK through point E, parallel to BC and AD. Since point E is the middle of CD, EP divides ABCD into two equal parallelograms. Spall = Sared = 130/2 = 65 cm2.

BE is the diagonal of РBCE, then Svse = Srvse / 2 = 65/2 = 32.5 cm2.

AE is the diagonal of APED, then Sade = Sared / 2 = 65/2 = 32.5 cm2.

Then Sall + Sade = 32.5 + 32.5 = 65 cm2.

Answer: The sum of the areas of the triangles BCE and ADE is 65 cm2.