# Convert Matric Units of Area to Hectares

 $\require{cancel}$ $\require{bbox}$

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 $\color{red}1$

$5680 \text{ dam}^2 = 5680 \text{ dam}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2}$
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 $\text{ ha}$