Question

100 square decameters = ________
A) 1 hectare (ha)
B) 10 square hectometer $(h{m^2})$
C) 1 square kilometer $(k{m^2})$
D) 100 square meter

Answer 1

A decametre is equal to 10 metres. We will use the formula of the area of a square to find the area of a square in different units.

Complete step by step answer
As mentioned in the hint, a decametre is equivalent to 10 metres. So, let us convert the area in question to metres and consequently all the options in metres too, and then we will compare.
So, 100 square decameters will be equal to
$A = 100\,d{m^2}$ which when converted to units of meters will be
$A = 100 \times {10^2}$
$\Rightarrow A = {10^4}\,{m^2}$
Hence the corresponding area of the amount given to us in meters will be ${10^4}\,{m^2}$ .
Now, in option (A), 1 hectare is equivalent to $10000\,{m^2}$ or ${10^4}\,{m^2}$ which is equal to the area given in question so option (A) is correct.
In option (B), a hectometer is equivalent to 100 meters. So, a square hectometer will have an area in meters as $10 \times {100^2} = {10^5}\,{m^2}$ which is not equal to the area in question, so option (B) is incorrect.
In option (C), 1 square kilometer will have dimensions in meters as ${10^6}\,{m^2}$ which is again not equal to the area in question.
In option (D), 100 square meters is not equal to ${10^4}$ square meters so option (D) is also incorrect.
Hence option (A) is the correct choice.

Note
We don’t need to directly remember the interconversion between different units of length such as decimetre, decametre, hectometre, etc. But we should remember their relation with the metre since the metre is the SI unit of length and we can use their interconversions to answer such questions.