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 = \( \Large 3\times 4=12 cm^{2} \)