In parallelogram ABCD, perpendicular BO is dropped on the diagonal AC. Find the area of the parallelogram

In parallelogram ABCD, perpendicular BO is dropped on the diagonal AC. Find the area of the parallelogram if AO = 8, OC = 6, BO = 4.

Let us determine the length of the AC diagonal.

AC = AO + CO = 8 + 6 = 14 cm.

Then the area of the triangle ABC will be equal to:

Saws = AC * ВO / 2 = 14 * 4/2 = 28 cm2.

Since the opposite sides of the parallelogram are equal and the opposite angles are equal, then the ACB triangle is equal to the ACD triangle on two sides and the angle between them and, therefore, Sас = Sасд = 28 cm.

Then Savs = Savs + Sasd = 28 + 28 = 56 cm2.

Answer: The area of the parallelogram is 56 cm2.