In a rhombus ABCD with a side of 5 cm, the angle between the side and the diagonal is 30 degrees.

In a rhombus ABCD with a side of 5 cm, the angle between the side and the diagonal is 30 degrees. Find the area of the rhombus.

The diagonals of the rhombus are the bisectors of the angles at its vertices, then the angle BAD = BAC * 2 = 30 * 2 = 60. Since AB = AD, as the sides of the rhombus, the triangle ABD is equilateral, AB = AD = BD = 5 cm.

Let us determine the length of the height of the AO.

AO = AB * √3 / 2 = 5 * √3 / 2, then AC = 2 * AO = 5 * √3 cm.

We define the area of the trapezoid in terms of the lengths of the diagonals.

Savsd = ВD * АС / 2 = 5 * 5 * √2 / 2 = 12.5 * √3 cm2.

Answer: The area of the rhombus is 12.5 * √3 cm2.

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