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

September 26, 2021 | education

| **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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