### Theory:

So far we have learned how to express the square units. Now, we shall learn the conversion of given square units.
Example:
Consider a rectangle of length of $$2$$ $$cm$$ and breadth $$1$$ $$cm$$. Find the area of the rectangle and convert its square units to $$mm^{2}$$.

Solution:

The area of the rectangle $$= l \times b$$

$$= 2 \times 1$$

$$= 2 \ sq. \ cm$$ or $$2 \ cm^{2}$$

Therefore, the area of the rectangle is $$2 \ cm^{2}$$.

Now, let us convert $$cm$$ to $$mm$$.

We know that $$1 \ cm =$$ $$10 \ mm$$.

Which implies that the length of the rectangle $$=$$ $$2 \ cm$$ $$=$$ $$2 \times 10 \ mm$$ $$=$$ $$20 \ mm$$

And the breadth of the rectangle $$=$$ $$1 \ cm$$ $$=$$ $$10 \ mm$$.

Thus, the area of the rectangle $$= l \times b$$

$$= 20 \times 10$$

$$= 200 \ mm^2$$

Hence, the area of the rectangle after conversion from $$cm$$ to $$mm$$ is $$200 \ mm^{2}$$.
Important!
The conversions can be simply remembered as follows:
• $$1 \ cm^2$$ $$=$$ $$10 \ mm$$$$\times$$$$10 \ mm$$ $$=$$ $$100 \ mm^2$$
• $$1 \ m^2$$ $$=$$ $$100 \ cm$$$$\times$$$$100 \ cm$$ $$=$$ $$10000 \ cm^2$$
• $$1 \ km^2$$ $$=$$ $$1000 \ m$$$$\times$$$$1000 \ m$$ $$=$$ $$1000000 \ m^2$$