Find the area of the rhombus if the angle B is 60 degrees, and one of the diagonals of the rhombus BD is 24 cm.

The area of a rhombus is the product of its diagonals divided by two.

S = 1/2 * d1 * d2;

one diagonal is known. Since the angle B is 60 °, the second diagonal divides the rhombus into two equal equilateral triangles. This means that the second diagonal of the rhombus is equal to its side.

We find the side from the cosine of the angle equal to half the angle.

cos 30 ° = 12 / d2;

d2 = 12 / cos 30 °;

d2 = 24/3 ^ (1/2) = 8 * 3 ^ (1/2);

S = 1/2 * d1 * d2 = 1/2 * 24 * 8 * 3 ^ (1/2) = 96 * 3 ^ (1/2).