In the parallelogram ABCD, the diagonal AC = 10 cm, the distance from vertex B

In the parallelogram ABCD, the diagonal AC = 10 cm, the distance from vertex B to this diagonal is half its length. Find the area of the parallelogram.

Let us prove that triangles ABC and AСD are equal.
Since the opposite sides of the parallelogram are equal, then AB = СD, BC = AD. The AC side of the triangles is common, then the ABC and AСD triangles are equal on three sides, then Sас = Sасd.
Let’s define the area of the triangle ABC.
By condition, ВO = AC / 2 = 10/2 = 5 cm.
Savs = AC * ВO / 2 = 10 * 5/2 = 25 cm2.
Then the parallelogram area is equal to: Savs = 2 * Savs = 2 * 25 = 50 cm2.
Answer: The area of the parallelogram is 50 cm2.