Definition of a Hectare
A hectare, abbreviated as ha, is defined by:
\[ 1 \, \text{ha} = 10,000 \, \text{m}^2 \]Since \( 1 \, \text{hm} = 100 \, \text{m} \), squaring both sides gives:
\[ (1 \, \text{hm})^2 = (100 \, \text{m})^2 \implies 1 \, \text{hm}^2 = 10,000 \, \text{m}^2 \]Hence, \( 1 \, \text{ha} = 1 \, \text{hm}^2 \), meaning converting an area to hectares is equivalent to converting it to square hectometers (\( \text{hm}^2 \)).
For length conversions between metric units, refer to the length conversion table.
Examples of Conversion to Hectares
Example 1
Convert \( 5,680 \, \text{dam}^2 \) to hectares (ha).
View Solution
Using the length conversion relationship, we know that \( 1 \, \text{hm} = 10 \, \text{dam} \). Squaring both sides:
\[ (1 \, \text{hm})^2 = (10 \, \text{dam})^2 \implies 1 \, \text{hm}^2 = 100 \, \text{dam}^2 \]This gives the conversion factor:
\[ \dfrac{1 \, \text{hm}^2}{100 \, \text{dam}^2} = 1 \]Now, rewrite the given area and multiply by this conversion factor:
\[ 5,680 \, \text{dam}^2 = 5,680 \, \text{dam}^2 \times \dfrac{1 \, \text{hm}^2}{100 \, \text{dam}^2} = \dfrac{5,680}{100} \, \text{hm}^2 = 56.8 \, \text{hm}^2 \]Since \( 1 \, \text{hm}^2 = 1 \, \text{ha} \):
\[ 5,680 \, \text{dam}^2 = 56.8 \, \text{ha} \]Example 2
Convert \( 125,000 \, \text{cm}^2 \) to hectares (ha).
View Solution
Since \( 1 \, \text{hm} = 10,000 \, \text{cm} \), squaring both sides gives:
\[ (1 \, \text{hm})^2 = (10,000 \, \text{cm})^2 \implies 1 \, \text{hm}^2 = 100,000,000 \, \text{cm}^2 \]This provides the conversion factor:
\[ \dfrac{1 \, \text{hm}^2}{100,000,000 \, \text{cm}^2} = 1 \]Multiply the given area by this factor:
\[ 125,000 \, \text{cm}^2 = 125,000 \, \text{cm}^2 \times \dfrac{1 \, \text{hm}^2}{100,000,000 \, \text{cm}^2} = \dfrac{125,000}{100,000,000} \, \text{hm}^2 = 0.00125 \, \text{hm}^2 \]Thus:
\[ 125,000 \, \text{cm}^2 = 0.00125 \, \text{ha} \]More Questions with Solutions
Problem 1
Convert \( 450,000 \, \text{m}^2 \) to hectares (ha).
View Solution
By definition, \( 1 \, \text{ha} = 10,000 \, \text{m}^2 \). The conversion factor is:
\[ \dfrac{1 \, \text{ha}}{10,000 \, \text{m}^2} = 1 \]Multiply and simplify:
\[ 450,000 \, \text{m}^2 = 450,000 \, \text{m}^2 \times \dfrac{1 \, \text{ha}}{10,000 \, \text{m}^2} = \dfrac{450,000}{10,000} \, \text{ha} = 45 \, \text{ha} \]Problem 2
Convert \( 4.5 \, \text{km}^2 \) to hectares (ha).
View Solution
We know that \( 1 \, \text{km} = 10 \, \text{hm} \). Squaring both sides gives:
\[ (1 \, \text{km})^2 = (10 \, \text{hm})^2 \implies 1 \, \text{km}^2 = 100 \, \text{hm}^2 \]Thus, the conversion factor is \( \dfrac{100 \, \text{hm}^2}{1 \, \text{km}^2} = 1 \):
\[ 4.5 \, \text{km}^2 = 4.5 \times 100 \, \text{hm}^2 = 450 \, \text{hm}^2 = 450 \, \text{ha} \]Problem 3
Convert \( 550 \, \text{dam}^2 \) to hectares (ha).
View Solution
Since \( 1 \, \text{hm} = 10 \, \text{dam} \), squaring both sides yields \( 1 \, \text{hm}^2 = 100 \, \text{dam}^2 \):
\[ 550 \, \text{dam}^2 = 550 \, \text{dam}^2 \times \dfrac{1 \, \text{hm}^2}{100 \, \text{dam}^2} = \dfrac{550}{100} \, \text{hm}^2 = 5.5 \, \text{hm}^2 = 5.5 \, \text{ha} \]Problem 4
Convert \( 8,910,000 \, \text{mm}^2 \) to hectares (ha).
View Solution
Since \( 1 \, \text{hm} = 100,000 \, \text{mm} \), squaring both sides gives \( 1 \, \text{hm}^2 = 10,000,000,000 \, \text{mm}^2 \):
\[ 8,910,000 \, \text{mm}^2 = 8,910,000 \times \dfrac{1 \, \text{hm}^2}{10,000,000,000 \, \text{mm}^2} = \dfrac{8,910,000}{10,000,000,000} \, \text{hm}^2 = 0.000891 \, \text{ha} \]