Find the area of a rhombus whose obtuse angle is 120 degrees, and the smaller diagonal is 6cm.

Since the rhombus is a parallelogram, the sum of its two adjacent angles is 180 °.

If the obtuse angle of a rhombus is 120 °, then its acute angle is 180 ° – 120 ° = 60 °. The diagonals of a rhombus are the bisectors of its corners; the smaller diagonal of the rhombus divides its obtuse angle in half. Therefore, the angle between the smaller diagonal and the side of the rhombus is 120 ° / 2 = 60 °. Thus, the smaller diagonal of the rhombus and its two sides form an equilateral triangle, since all the angles of this triangle are 60 °, which means that the side of the rhombus is equal to its smaller diagonal.

We find the area of ​​the rhombus by the formula:

S = a ^ 2 * sin 60 ° = 6 ^ 2 * √3 / 2 = 36 * √3 / 2 = 18√3 ≈ 31.18 cm2.