In parallelogram ABCD, diagonal BD is perpendicular to its side AB, segment DF is the height drawn from vertex D

In parallelogram ABCD, diagonal BD is perpendicular to its side AB, segment DF is the height drawn from vertex D to side BC. Calculate the area of the parallelogram if DF = 8 cm, FC = 4 cm.

Since, by condition, the diagonal BD is perpendicular to AB, and the side of CD is parallel to AB, as the opposite sides of the parallelogram, then BD is perpendicular to CD.

Then the height DF is drawn to the hypotenuse from the vertex of the right angle, which means DF ^ 2 = CF * BF.

BF = DF ^ 2 / CF = 64/4 = 16 cm.

Then BC = BF + CF = 16 + 4 = 20 cm.

Determine the area of the parallelogram. Savsd = ВС * DF = 20 * 8 = 160 cm2.

Answer: The area of the parallelogram is 160 cm2.