Find the area of the rhombus ABCD if its height VK is 6 cm, and the angle ABC is 120 degrees.

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

∠ BAD = 180 ° – ∠ABC = 180 ° – 120 ° = 60 °.

In a right-angled triangle BKA: AB – hypotenuse, BK – leg opposite to BAD angle. The ratio of the opposite leg to the hypotenuse is the sine of the angle, therefore:

BK / AB = sin ∠ BAD;

AB = BK / sin ∠ BAD = 6 / sin 60 ° = 6 / (√3 / 2) = 12 / √3 = 4√3 cm – rhombus side.

The area of a rhombus is defined as the product of its height and side length:

S = AB * BK = 4√3 * 6 = 24√3 ≈ 41.57 cm2 – the required area of the rhombus.