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In this article, we will learn what are the units of area and how to convert one unit to another. But before proceeding to discuss the units, first, we will see what an area is.
What is Area?
The area can be defined in the following two ways:
"The quantity that depicts the extent of two-dimensional shape or figure in the plane is known as area"
Or
"A space taken by a flat shape or an object is called the area"
The concept of the area can also be comprehended by considering small squares of equal sizes. The number of squares that are covered by the shape or its surface is the area of that shape. For example, consider a rectangle that is placed on a grid. Suppose each square in the grid has an area of $1 cm^2$. If 30 squares fit into a closed rectangle on a grid, then we can say that the area of the rectangle is $30 cm^2$.
In geometry, we come across different shapes like squares, rectangles, and triangles, etc. All these shapes have different formulas for the calculation of their areas.
An area measures the amount of space inside a shape. Knowing how to calculate an area has many useful applications in our daily life. For instance, if you know the area of a wall, then you can calculate the amount of paint needed for the walls. Similarly, if you know the area of the floor of your kitchen, then you can easily compute the number of tiles needed to cover that floor.
Surface Area
You might have heard the term "surface area". The procedure of calculating the surface area of an object is different from calculating the area of an object. The primary difference between area and surface area is that area is measured for a two-dimensional object or a flat shape. On the other hand, a surface area is measured for 3-dimensional (3D) shapes. A 3D shape can have many 2D shaped faces. Since the surface area depicts the total area covered by the surface of an object, therefore a surface area is an aggregate of the areas of all the faces of the object.
For instance, consider a cuboid. The number of rectangular faces in a cuboid is six. Therefore, to measure the surface area of a cuboid, we will add the areas of all the rectangular faces. The units of area and surface area are the same.
Now, that we know what an area of an object is, let us proceed to discuss the SI units of area.
SI Units of Area
The fundamental unit for measuring area under metric system is the square meter. It is equal to the area of a square whose sides measure 1 meter.
| square kilometer | km² | 1,000,000 m² |
| square hectometer | hm² | 10,000 m² |
| square decameter | dam² | 100 m² |
| square meter | m² | 1 m² |
| square decimeter | dm² | 0.01 m² |
| square centimeter | cm² | 0.0001 m² |
| square millimeter | mm² | 0.000001 m² |
Note that each unit is 100 times larger than the previous.
Land Area Measurements
The common units to measure the area of land are given below:
Hectare
The hectare is equivalent to the square hectometer.
1 ha = 1 hm² = 10,000 m²
Are
The are is equivalent to the square decameter.
1 a = 1 dam² = 100 m²
Centiare
The centiare is equivalent to the square meter.
1 ca = 1 m²'
Unit Conversion
We can convert one unit of the area into another by multiplying or dividing the unit by one followed by as many pairs of zeros as there are places between them. For example, convert $2.5 hm^2$ to $m^2$.
1 square hectometer = 10,000 square meters
2.5 square hectometers = 2.5 x 10000
= $25000 m^2$
In the next section, we will solve some examples in which we will convert one unit of area into another.
Example 1
Convert $35,000 mm^2$ into $m^2$.
Solution
Since $mm^2$ is smaller than $m^2$, therefore we will be dividing to convert the unit:
$1 mm^2 = 0.000001 m^2$
$ 1 m ^2 = \frac{1}{1000000} mm^2$
35000 square millimeters will be divided by 1000,000 to get the answer in square meters:
$35000 mm^2 = \frac{35000}{1000,000} m^2$
= $0.035 m^2$
Example 2
Convert $19 m^2$ into $dam^2$,
Solution
$m^2$ is smaller than $dam^2$ because $1 dam^2 = 100 m^2$.
$1 dam ^2 = 100 m^2$
$19 m^2 = \frac{19}{100} dam^2$
$ = 0.19 dam^2$
Example 3
Convert $510 cm^2$ to $km^2$
Solution
In this example, first, we will convert $cm^2$ to $m^2$, and then $m^2$ to $km^2$.
$1 cm^2 = 0.0001 m^2$
$510 cm^2 = \frac{510}{10000} m^2$
Remember that instead of dividing the number with one followed by zeroes, you can also multiply the number by 0.0001. The answer will be the same in both cases.
= $ 0.051 m^2$
Now we have the amount in $m^2$, so we will proceed to convert it into the $km^2$:
$1 km ^2 = 1000,000 m^2$
$0.051 m^2 = \frac{0.051}{1000,000} km^2$
= $0.000000051 km^2$
We can write the answer in scientific notation like this:
= $5.14$ x $10 ^ {-8} km^2$
Example 4
Convert $89 dam^2$ to $mm^2$.
Solution
In this example, first, we will convert $dam^2$ to $m^2$ and then $m^2$ to $mm^2$. Since $dam^2$ is a bigger unit and $m^2$ is the smaller unit, therefore we will use the arithmetic operation of multiplication for conversion:
$ 1 dam^2 = 100 m^2$
$89 dam^2 = 89 \cdot 100 m^2$
89 dam will be multiplied by 100 to get the value in meter square:
= $8900 m^2$
Now, we have the value in $m^2$, so we will convert it into $mm^2$. Again, $mm^2$ is smaller than $m^2$, so we will use multiplication here:
$ 1m ^2 = 1000,000 mm^2$
$8900 m^2 = 8900 \cdot 1000,000 mm^2$
= $8900,000,000 mm^2$
We can write the answer in scientific notation like this:
= $8.9$ x $10 ^9 mm^2$
Example 5
Convert $55 hm^2$ to $dm^2$.
Solution
In this example, first, we will convert $hm^2$ to $dm^2$ and then $m^2$ to $dm^2$. Since $hm^2$ is a bigger unit and $m^2$ is the smaller unit, therefore we will use the arithmetic operation of multiplication for conversion:
$ 1 hm^2 = 10,000 m^2$
$55 hm^2 = 55 \cdot 10,000 m^2$
= $550,000 m^2$
Now, we have the value in $m^2$, so we will convert it into $dm^2$. Again, $dm^2$ is smaller than $m^2$, so we will use multiplication here:
$ 1 m ^2 = 100 dm^2$
$550,000 m^2 = 550,000 \cdot 100 dm^2$
= $550,00000 dm^2$
We can write the answer in scientific notation like this:
= $5.5$ x $10 ^7 dm^2$
Example 6
According to the law, a building's ground floor area cannot cover more than one-third of the area of the land it is built on. John wants to construct a building on 45- are land. What is the maximum land in meter squares that can be occupied by the ground floor of the building?
Solution
The area of the land = 45 are
The maximum area a ground floor can cover = $\frac{1}{3} \cdot 45 = 15$ Ares
Now, we will convert Ares into meter squares.
1 Are = 100 $m^2$
15 Ares = 1500 $m^2$
Hence, the maximum area of the ground floor of the building can be 1500 ^m^2$ as per the law.
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