Side of the rhombus = 8.6 cm and one of the corners of the rhombus = 30 degrees. Find the area of the rhombus.

Suppose that in the rhombus ABCD, the side AD = 8.6 cm, and the angle ∠BAD = 30 °.

Let us lower the height of the ВН to the base of AD and consider the resulting right-angled triangle ΔАВН (∠ВНА = 90 °). In it, the ВН leg is equal to half of the AB hypotenuse by the property of the leg, which lies opposite the angle ∠BAD = 30 °; and the side AB = AD = 8.6 cm – according to the property of the sides of the rhombus. We get: BH = 8.6 cm: 2; BH = 4.3 cm.

To find the area of a rhombus, we find the product of the length of the base of the rhombus by the length of its height, that is, S = AD · BH or S = 8.6 cm · 4.3 cm; S = 36.98 cm².

Answer: The area of the rhombus is 36.98 cm².