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 eNotes educator| Certified Educator

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.


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


Compute angle A using the sine trigonometric function:




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



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

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