The degree measure of one of the corners of the rhombus is 120 degrees.

| September 23, 2021 | education

The degree measure of one of the corners of the rhombus is 120 degrees. Calculate the area of a rhombus if the area of a circle inscribed in it is 3pi cm2

The area of the circle is equal to: Sokr = n * R ^ 2 = 3 * n.

R ^ 2 = 3.

R = √3.

The KM segment is the diameter of the circle and is equal to 2 * R.

KM = 2 * √3.

The height of the rhombus AH = KM = 2 * √3.

In a rhombus, the opposite angles are equal, then the angle ADC = (360 – 120 – 120) / 2 = 60.

Consider a right-angled triangle АНD, in which the leg АН = 2 * √3, and the angle АDН = 60.

SinADN = AH / AD.

√3 / 2 = 2 * √3 / AD.

АD = 2 * √3 / (√3 / 2) = 4 cm.

Since the rhombus has the same lengths of the sides, then DC = AB.

The area of the rhombus will be equal to:

S = DC * AH = 4 * 2 * √3 = 8 * √3 cm2.

Answer: The area of the rhombus is 8 * √3 cm2.



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