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 \(mm^{2}\).
 
Figure_1.png
 
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:
  • \(1 \ cm^2\) \(=\) \(10 \ mm\)\(\times\)\(10 \ mm\) \(=\) \(100 \ mm^2\)
  • \(1 \ m^2\) \(=\) \(100 \ cm\)\(\times\)\(100 \ cm\) \(=\) \(10000 \ cm^2\)
  • \(1 \ km^2\) \(=\) \(1000 \ m\)\(\times\)\(1000 \ m\) \(=\) \(1000000 \ m^2\)