Area Units

Area

Definition Area

The area of a shape is how much space it covers on a flat surface.
We measure area by counting how many square units fit inside the shape.

To find the area of a shape, we can place it on a grid and count the total number of squares it covers.
You can think of it like tiling a floor — the area is the total number of tiles you use.

Example

Find the area of the green shape. Each small square in the grid is 1 square unit.

Answer

To find the area, we count each square unit inside the shape.

There are 4 small squares inside the shape.
So, the area is 4 square units.

Units of Area

Discover

When we measure area, it is important to use standard units so that everyone gets the same measurement. Non-standard units, such as books or tiles of different sizes, can give different answers because they are not all the same size. For area, we use standard units like the square centimeter and the square meter.

Definition Units of Area

Area is measured in square units. The standard units are based on the metric system.

Square Kilometer ($\mathrm{km}^2$): The area of a square with sides 1 km long. Used for very large areas like cities or national parks.
Square Meter ($\mathrm{m}^2$): The area of a square with sides 1 m long. Used for areas like rooms, gardens, or classrooms.
Square Centimeter ($\mathrm{cm}^2$): The area of a square with sides 1 cm long. Used for small surfaces like book covers or photos.
Square Millimeter ($\mathrm{mm}^2$): The area of a square with sides 1 mm long. Used for very tiny areas.

Conversion of Area Units

Discover

Let's see how area units are related. Consider a square with an area of 1 cm². Since 1 cm = 10 mm, each side of this square is 10 mm long.

Each small square is 1 mm². To find the area in mm², we multiply its length in mm by its width in mm:$$ \begin{aligned} 1 \, \mathrm{cm}^2 &= 1 \, \mathrm{cm} \times 1 \, \mathrm{cm} \\ &= 10 \, \mathrm{mm} \times 10 \, \mathrm{mm} \\ &= 100 \, \mathrm{mm}^2 \end{aligned} $$So, 1 cm² is equal to 100 mm². The conversion factor is squared!

Proposition Conversion of Area Units

Because we multiply two lengths to get an area, the conversion factors are squared.

$1 \, \text{cm}^2 = (10 \times 10) \, \text{mm}^2 = \mathbf{100} \, \text{mm}^2$
$1 \, \text{m}^2 = (100 \times 100) \, \text{cm}^2 = \mathbf{10,000} \, \text{cm}^2$
$1 \, \text{km}^2 = (1000 \times 1000) \, \text{m}^2 = \mathbf{1,000,000} \, \text{m}^2$

Method Converting Using Multiplication or Division

Use multiplication to go from a larger unit to a smaller one (like square meters to square centimeters).
Use division to go from a smaller unit to a larger one (like square centimeters to square meters).

Method Converting Using a Place Value Table

For area, each unit in the place value table is split into two columns. Let's convert 10.5 m² to cm².

Draw the area conversion table. Each unit has two columns.
Place the number in the table. The rule is: the digit in the ones place goes into the right-hand column of the starting unit. For 10.5 m², the ones digit is 0, so it goes in the right-hand column of m². Then place the other digits in the neighbouring columns, keeping their order (tens to the left, decimal digits to the right).
Move the decimal point to the right side of your target unit's columns. Our target is cm². Fill any empty columns with zeros.
Read the final number. The decimal point is now at the far right.So, 10.5 m² = $105\,000$ cm².