In a rhombus, the side is 10, one of the diagonals is 10, and the angle from which this diagonal exits

In a rhombus, the side is 10, one of the diagonals is 10, and the angle from which this diagonal exits is 120 degrees. Find the area of the rhombus divided by √3.

In a right-angled triangle ABO, leg OB = BD / 2 = 10/2 = 5 cm, then, according to the Pythagorean theorem, leg AO ^ 2 = AB ^ 2 – BO ^ 2 = 100 – 25 = 75.

AO = 5 * √3 cm.

Then the diagonal AC = 2 * AO = 2 * 5 * √3 = 10 * √3 cm.

Determine the area of the rhombus.

S = АС * ВD / 2 = 5 * √3 * 10 = 50 * √3 cm.

Then the area divided by the root of three is 50 cm2.

Answer: 50 cm2.