# Find the area of a rhombus with a side of 12 cm and an obtuse angle of 150 degrees

October 3, 2021 | education

| Let’s use the formula S = (a ^ 2) * sin of the acute angle of the rhombus. Let’s find the corner first. The diagonals of a rhombus are the bisectors of its angles, which means 150: 2 = 75 degrees. The diagonals of the rhombus intersect at right angles (90 degrees). from here you can find the degree measure of the acute angle: 75 degrees + 90 degrees + x degrees = 180 degrees;

x degrees = 180-75-90;

x = 15 degrees. Hence the acute angle of the rhombus is 15 degrees * 2 = 30 degrees.

Find the area: S = 12 ^ 2 * sin 30 degrees = 144 * 1/2 = 72 cm ^ 2

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