The diagonal of the parallelogram is 5 cm, and is perpendicular to the 3 cm side of the parallelogram.

The diagonal of the parallelogram is 5 cm, and is perpendicular to the 3 cm side of the parallelogram. Find the area of the parallelogram.

1. The tops of the parallelogram – A, B, C, D. AB = 3 centimeters. BD = 5 centimeters. Diagonal BD is perpendicular to side AB.

2. According to the problem statement, sides AB and BD of triangle ABD are perpendicular. Taking this into account, we calculate the area (S) ΔАВD:

S ΔABD = AB x BD / 2 = 3 x 5/2 = 7.5 centimeters².

3. Diagonal ВD, according to the properties of a parallelogram, divides it into two equal triangles:

ΔABD and ΔBCD. With this in mind, we calculate the area of the parallelogram:

4. S parallelogram ABCD = 7.5 х 2 = 15 centimeters².