Question

How is the unit of ${\text{c}}{{\text{m}}^2}$ related to the S.I. unit of area ?

Answer 1

The present form of the metric system is the International System of Units (SI, shortened from the French Système international (d'unités)). It is the only method of measurement recognised by practically every country on the planet. It is made up of a logical system of measuring units that starts with seven basic units.

Complete step by step answer:
The SI unit of length is the metre (symbol m). It is calculated by taking the fixed numerical value of the speed of light in vacuum, c, and converting it to $m{s^{ - 1}}$, where the second is specified in terms of $\Delta v\,c$. The metre was first defined in 1793 as one ten-millionth of the distance in a great circle from the equator to the North Pole, implying that the Earth's circumference is around 40000 km. In 1799, a prototype metre bar was used to redefine the metre (the actual bar used was changed in 1889). The metre was redefined in 1960 in terms of a certain number of wavelengths of a krypton-86 emission line.

A centimetre or centimetre is a unit of length in the metric system, equal to one tenth of a metre, centi being the SI prefix denoting a factor of $\dfrac{1}{{100}}$. In the now-deprecated centimetre–gram–second system of units, the centimetre was the basic unit of length. $1\,m$ equals $100\,cm$
Hence $1\,cm = \dfrac{1}{{100}}\,m$
$1\;{\text{c}}{{\text{m}}^2} = \left( {\dfrac{1}{{100}}\;{\text{m}}} \right) \times \left( {\dfrac{1}{{100}}\;{\text{m}}} \right) \\\ \therefore 1\;{\text{c}}{{\text{m}}^2}= \dfrac{1}{{10000}}\;{{\text{m}}^2}$

Hence, SI unit of area is ${m^2}$.

Note: The CGS system was substantially superseded by the MKS system, which was extended and superseded by the International System of Units, which was based on the metre, kilogramme, and second (SI). SI is the sole system of units used in many sectors of research and engineering, while CGS is still widely used in several subfields.