The sides of the parallelogram are 4 cm and 5 cm, the angle between them is 45 °. Find the height of the parallelogram.

From the condition it is known that the sides of the parallelogram are 4 cm and 5 cm, and it is also known that the angle between them is 45 °. In order to find the height of the parallelogram we will apply two formulas to calculate the area of the parallelogram.

So, the first formula for finding the area:

S = a * b * sin A.

Substitute the values and find:

S = 4 * 5 * sin 45 ° = 20 * √2 / 2 = 10√2 cm ^ 2.

S = a * ha.

The area of the parallelogram is equal to the product of the side and the height dropped on it.

Height drawn to the side with a length of 4 cm:

ha = S / a = 10√2 / 4 = 2.5√2 cm.

Height drawn to the side with a length of 5 cm:

hb = S / b = 10√2 / 5 = 2√2 cm.