Question

100 square metres = ______.
A. 1 square centimetres
B. 1 are
C. 1 hectare
D. 10 hectares

Answer 1

Hint: Recall that all units mentioned in the question $m^2,\; cm^2,\; are(a),\; hectare(ha)$ are all units of area, with the last three being the commercial units of area. Note that this relation between $m^2$ and the commercial units is just empirical and cannot be mathematically derived. We know that $1\;m^2$ is the area enclosed by two sides of length $1\;m$ each. This means that $100\;m^2$ is the area enclosed by to sides of length $10\;m$ each. To this end, using the fact that $1\;ha = 10^4\;m^2$ arrives at the appropriate relation.

Complete step by step answer:
We know the $1\;cm =10^{-2}\;m$
This means that $(1\;cm)^2 = (10^{-2}\;m)^2$
$\Rightarrow 1\;cm^2 = 10^{-2}\;m^2$
Therefore, the first option is wrong.
Now, Are is a unit of area that is generally associated with the measurement of dimensions of a land area. It was defined as part of an older form of the metric system decreed in 1795 in France, but is now outside the SI. However, its multiple, which is the hectare (equal to 100 acres) still remains to be used as the principle unit of land measurement in most parts of the world. The Are can also be defined by standard metric prefixes to the original base unit such as decimilliare $ = 10^{-5}\;ares$, decare $ = 10\;ares$ and so on.
The centiare is defined to be $ = 1m^2$. The deciare is defined to be $ = 10m^2$. Following this is the Are, which is equal to an area enclosed by a $10m \times 10m$ area, which is equal to 100 square metres. This relation is purely definitive and cannot be mathematically derived.
To this end we have hectare defined as $=10^4\;m^2 = 10^2ares$.
Therefore, $100\;m^2 = 1\;are$.

So, the correct answer is “Option B”.

Note: Note that in practice, the hectare is fully derived from the SI, being equivalent to a square hectometre.
$1\;hm = 10^2\;m$
$1\;hm^2 = 10^4\;m^2 = 1ha$
Other prominently used land measurement unit is the acre, where $1\;acre = 0.405\;ha$