Find the area of a square whose side is $4.1\,cm$?

Hint: We find the formula of finding area of a square. We compare their heights and the base. This gives the relation between the area of the square as the square of the length of any side. We take the value of $4.1\,cm$ and find the area.

Complete step by step answer:
We draw a square $PQRS$ whose sides are $4.1\,cm$.

Now when we take a square, we can define it in the form of a rhombus where a rhombus converts into a square with its all angles being equal to each other and also its sides are equal. This means the angle of the square becomes equal to $\dfrac{\pi }{2}$.

For a square it is the square value of one side. The general formula is the multiplication of two consecutive sides and in the case of squares both are of same length. So, if the side of the square is $a$ unit, then the area will be ${{a}^{2}}$ square units. For square $PQRS$, we find the area with change of value of $a=4.1$. Putting the value, we get ${{a}^{2}}={{\left( 4.1 \right)}^{2}}=16.81$ square cm.

Therefore, the area of a square whose side is $4.1$ is $16.81$ square cm.

Note: We need to be careful about the proof of the parallelogram. The proof gives us relation between the heights. The height for the square is the side as that creates the right angle on the base. Rhombus has all sides equal in length but square has all sides equal in length and also all the interior angles are right angles. Thus, they are not similar. But we can say that a rhombus is a pushed over square.