Convert Matric Units of Area to Hectares

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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 \( \text{ ha} \).

Metric Units of Length Conversion Table
Table. 1 - Metric Units of Length Conversion Table


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 \( \color{red}1 \)

\( 5680 \text{ dam}^2 = 5680 \text{ dam}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} \)
Cancel \( \text{ dam}^2 \) on the right
\( 5680 \text{ dam}^2 = 5680 \cancel{\text{ dam}^2} \times \displaystyle \frac{1 \text{ hm}^2}{100 \cancel{ \text{ dam}^2}} \)
Simplify
\( 5680 \text{ dam}^2 = \displaystyle \frac{5680 \times 1 \text{ hm}^2 }{100} \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 5680 \text{ dam}^2 = 56.8 \text{ hm}^2 = 56.8 \text{ ha} } \]


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 \( \color{red}1 \)

\( 125000 \text{ cm}^2 = 125000 \text{ cm}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} \)
Cancel \( \text{ cm}^2 \)
\( 125000 \text{ cm}^2 = 125000 \cancel{ \text{ cm}^2} \times \displaystyle \frac{1 \text{ hm}^2}{100000000 \cancel{ \text{ cm}^2}} \)
Simplify
\( 125000 \text{ cm}^2 = \displaystyle \frac{125000 \times 1 \text{ hm}^2 }{100000000} \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 125000 \text{ cm}^2 = 0.00125 \text{ hm}^2 = 0.00125 \text{ ha} } \]



Questions with Solutions

Convert the following

  1.    \( 450000 \text{ m}^2 \) to \( \text{ ha} \)
  2.    \( 4.5 \text{ km}^2 \) to \( \text{ ha} \)
  3.    \( 550 \text{ dam}^2 \) to \( \text{ ha} \)
  4.    \( 8910000 \text{ mm}^2 \) to \( \text{ ha} \)
  5.    \( 900000 \text{ dm}^2 \) to \( \text{ ha} \)





More References and links

  1. Metric Units of Length Conversion
  2. Convert Metric Units of Area
  3. Factor of Conversion of Units
  4. SI Prefixes Used with Units
  5. Convert Metric Units of Area
  6. Online Calculator to Convert Time from Decimal to Hours, Minutes and Seconds
  7. Online Calculator to Convert Time From Hours, Minutes and Seconds to Decimal
  8. Convert Units of Measurements
  9. Units Conversion and Calculators