The are of a rombus is 6 cm^2. The area of the inscribed circle is 3 cm^2. what are the angles of the rombus?

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flbyrne | (Level 3) Assistant Educator

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The height of the rhombus is equal to the diameter of the circle. Compute the radius of the circle given its area using:

`A=pid^2/4`  or `d=2sqrt(A/pi)`

Substitute `3cm^2` for A to obtain d.

`d=2sqrt(3/pi)=1.95 cm`

The area A of a rhombus is equal to the product of its side s by its height h.

A=sxh

Determine the side s by substituting `6cm^2` for A and `1.95cm` for h and solving for s.

`s=(6cm^2)/(1.95cm)=3.08cm`

Compute angle A using the sine trigonometric function:

`sinA=h/s`

`A=sin^-1(h/s)`

`A=sin^-1(1.95/3.08)=39.28`

The sum of all the angles of the rhombus is equal to 360 degrees. Compute the value of angles B and D.

`B+D=2B=360-2(39.28)=281.44`

`B=D=140.72`

Therefore the angles are A=C=39.28 degrees and B=D=140.74 degrees.

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