Find the area of a rhombus if its obtuse angle is 120 and the smaller diagonal is 6 cm.

univerkov | January 11, 2021 | education

In a rhombus, the sum of its adjacent angles is 1800, then the angle ВAD = (180 – ABC) = (180 – 120) = 60.
In the AED triangle, AB = AD as the sides of the rhombus, and the AED angle = 60, then the AED triangle is equilateral, AB = AD = ВD = 6 cm.
Determine the area of the rhombus.
Savs = AВ *AD * SinВAD = 6 * 6 * Sin60 = 36 * √3 / 2 = 18 * √3 cm2.
Answer: The area of the rhombus is 18 * √3 cm2.

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