The perimeter of the rhombus is 20 cm. Find the distance between the opposite sides

| September 5, 2021 | education

The perimeter of the rhombus is 20 cm. Find the distance between the opposite sides of the rhombus if one of its diagonals makes an angle of 75 degrees with the side.

Knowing the perimeter of the rhombus, we can find the length of its side:

a = P / 4 = 20/4 = 5 cm.

It is known that the diagonals of a rhombus are the bisectors of its angles, therefore, if one of the diagonals makes an angle of 75 ° with the side of the rhombus, then this angle of the rhombus is 75 * 2 = 150 °.

The area of ​​a rhombus can be found as the product of the square of the side and the sine of the angle between them:

S = a2 * sin α = 52 * sin 150 ° = 25 * 0.5 = 12.5 cm2.

Obviously, the distance between the opposite sides of the rhombus is the height of the rhombus. Since the area of ​​a rhombus is also determined as the product of the length of the side by the height, we can find the height by dividing the value of the area by the length of the side:

h = S / a = 12.5 / 5 = 2.5 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.