Given that the length of each side of a rhombus is 8 cm and that an interior angle measures 60°. Find the exact area of the inscribed circle.
The area of the circle inscribed in a rhombus.
The side length of the rhombus is 8 cm.
The angle of the rhombus is 60°.
The diagonals of the rhombus AC and BD bisect each other with right angles at the center of the circle.
The diagonals divide the rhombus in to four 30-60-90 triangles.
In the triangle AOB, We know AB = 8.
In 30-60-90 triangles, the side length ratio is .
Therefore, the length of OB = 4 and OA is .
Now, draw a perpendicular OP (radius of the circle) to the side AB of rhombus.
It forms a new 30-60-90 right angle triangle AOP.
Now, we know one side OA is
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