all the vertices of a rhombus lie on a circle. find the area of the rhombus if the area of the circle is 1256cm²

Given: All the vertices of a rhombus lie on the circle

Let ABCD be the rhuombus.

In a rhombus opposite angles are equal

⇒ ∠A = ∠C  ...... (1)

but in a cyclic quadrilateral opposite angles are supplementary

⇒ ∠A + ∠C = 180°  ...... (2)

from (1) and (2) we get

Hence ABCD is a square.

and diagonal AC is the diameter              (∵ converse of angle in a semicircle is right angle)

Now area of circle = 1256 cm² 

⇒ π radius² = 1256 cm² 

Now in right ∆ ABC

AB² + BC² = AC² = (Diameter)² 

⇒ 2(side)² = (2 radius)² 

⇒ side² = 2 radius² 

Hence area of ABCD = side² = 2 radius²