# In a rhombus with an area of 98 cm2, one of the angles is 150 degrees. find the perimeter of the diamond.

August 24, 2021 | education

| The area of a rhombus can be defined as the product of the square of the side and the sine of the angle between them:

S = a ^ 2 * sin α.

Knowing the area of the rhombus and the angle between the sides, we can find the length of the side:

a ^ 2 = S / sin α = 98 / sin 150 ° = 98 / 0.5 = 196 = 142;

a = 14 cm – rhombus side.

The perimeter of the rhombus is equal to the sum of the lengths of all sides, and since all sides of the rhombus are equal to each other, then:

P = 4 * a = 4 * 14 = 56 cm – the desired perimeter of a given rhombus.

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