# 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 $$\text{ ha}$$.

## 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 $$\text{ ha}$$