In a rectangle, the diagonal is 12 cm and the angle between the diagonals is 30 degrees, find the area of the rectangle.

1. A, B, C, D – the vertices of the rectangle. AC and VD are diagonals. O is the point of their intersection.

∠АВ = 30 °.

2. In a rectangle, the diagonals are:

AC = BD = 12 centimeters.

3. According to the properties of a rectangle, its area (S) is calculated by the formula:

S = AC x BD / 2 x sine SAOB.

sine ∠AOB = sine 30 ° = 1/2.

S = 12 x 12/2 x 1/2 = 144: 4 = 36 centimeters².

Answer: S = 36 centimeters².