ABCD be the rectangle inscribed in the circle of diameter 5 cm.
Diameter = Diagonal of rectangle
Now, let x and y be the lengths and breadths of rectangle, respectively.
Now, in \( \Large \triangle ABD \)
\( \Large AB^{2}+AD^{2}=(5)^{2} \)
=> \( \Large x^{2}+y^{2} \)=25
Since, they form Pythagoras theorem.
So,x=4 and y=3
Area of rectangle = \( \Large 3\times 4=12 cm^{2} \)