Convert metric units of area, such as, \( \text{m}^2, \text{cm}^2, \text{mm}^2, \text{km}^2, ...\) to hectares ( \( \text{ ha} \) ), examples with solutions are presented including more More questions with solutions .
A hectare whose abbreviation is written as \( \text{ ha} \) is defined by
\[ 1 \text{ ha} = 10000 \text{ m}^2\]
and since
\[ 1 \text{ hm} = 100 \text{ m}\]
Square both sides
\[ (1 \text{ hm})(1 \text{ hm}) = (100 \text{ m})(100 \text{ m})\]
Simplify the above and rewrite as
\[ 1 \text{ hm}^2 = 10000 \text{ m}^2 \]
Hence
\[ 1 \text{ ha} = 1 \text{ hm}^2\]
and therefore conversting to \( \text{ ha} \) is the same as converting to \( \text{ hm}^2 \)
The table shown below helps in finding factors of conversion between metric units of length which in turn helps converting units of area to \( \text{ hm}^2 \) and therefore to \( \text{ ha} \).
Examples of Conversion to \( \text{ ha} \) with Solutions
For a thorough understanding of the conversion, we show all steps with details in examples 1 and 2.
Example 1
Convert \( 5680 \text{ dam}^2 \) to \( \text{ ha} \)
Solution to Example 1
We are given \( \text{ dam}^2 \), we therefore use Table 1 to find the conversion between \( \text{ dam} \) and \( \text{ hm} \). Using the Table 1 above, we have
\( 1 \text{ hm} = 10 \text{ dam} \)
Square both sides
\( (1 \text{ hm})(1 \text{ hm}) = (10 \text{ dam})(10 \text{ dam}) \)
Simplify and rewrite as
\( 1 \text{ hm}^2 = 100 \text{ dam}^2 \)
which gives the factor of conversion
\[ \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} = 1 \]
Rewrite the given area \( 5680 \text{ dam}^2 \) as
\( 5680 \text{ dam}^2 = 5680 \text{ dam}^2 \times \color{red}1 \)
Substitute \( \color{red} 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} \) which is also equal to \( \color{red}1 \)
Example 2
Convert \( 125000 \text{ cm}^2 \) to \( \text{ ha} \)
Solution to Example 2
We are given \( \text{ cm}^2 \), we therefore use Table 1 to find the conversion between \( \text{ cm} \) and \( \text{ hm} \)
\( 1 \text{ hm} = 10000 \text{ cm} \)
Square both sides
\( (1 \text{ hm})(1 \text{ hm}) = (10000 \text{ cm})(10000 \text{ cm}) \)
Simplify and rewrite as
\( 1 \text{ hm}^2 = 100000000 \text{ cm}^2 \)
which gives the factor of conversion
\[ \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} = 1 \]
Rewrite the given area \( 125000 \text{ cm}^2 \) as
\( 125000 \text{ cm}^2 = 125000 \text{ cm}^2 \times \color{red}1 \)
Substitute \( \color{red} 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} \) since it is equal to \( \color{red}1 \)