The diagonals of the parallelogram are equal to m and n, the angle between them is 60 degrees

The diagonals of the parallelogram are equal to m and n, the angle between them is 60 degrees, find the area of the parallelogram.

1. There is a formula: the area of a parallelogram is half the product of its diagonals by the sine of the angle between them.

2. Let us calculate the area S of a given parallelogram if, according to the problem statement, it is known that its diagonals are equal to m and n, and the angle between them is 60 °.

To do this, according to the table of trigonometric functions, we find sin 60 ° = √3 / 2, and then we find what the area is equal to.

S = 1/2 * n * m * √3 / 2 = √3 / 4 * m *.

Answer: The area of the parallelogram is √3 / 4 * m * n.