Surface Area Units or Area Measurements

Every two-dimensional object has an area. For example, every square, rectangle or circle has an area.

$\text{cm}^2$ (square centimeter), $m^2$ (square meter), $\text{km}^2$ (square kilometer).

These units are different, but they are related:

$1\text{km}^2=1,000,000\text{m}^2$

$1\text{m}^2=10,000\text{cm}^2$

Understanding the relationship between these units is key, but there's no need to memorize it—we can quickly calculate it when needed.

Let's say we want to calculate how many $\text{cm}^2$ are in $1\text{m}^2$. We’ll draw a square whose sides each measure $1$ meter:

To calculate the area of the square, we need to multiply the length of one side by the other (this is a well-known formula). In our case:

The area of the square $=1\text{m}\times1\text{m}$.

The result is $1$ m² or, writing it another way:

$S=1\text{m}^2$

Remember, surface area measurements are always to the second power!

Now let's do the same exercise using surface units in $\text{cm}$.

That is:

Each side of the square is $1\text{m}$, which is the same as $100\text{cm}$. Let's calculate the area again:

The area of the square $=100\text{cm}\times100\text{cm}=10,000\text{cm}^2$

Or, writing it another way:

$S=100\text{cm}\times100\text{cm}=10,000\text{cm}^2$

So the first time, we found that the area of the square is $1$ square meter, and the second time the same area is equivalent to $10,000\text{cm}^2$.

We can deduce that:

$1\text{m}^2=10,000\text{cm}^2$

We can make the same calculation directly without drawing. Let's write it this way:

$1\text{m}^2=1\text{m}\times1\text{m}=100\text{cm}\times100\text{cm}=10,000\text{cm}^2$

This way, we can always convert between different measurements of area. Now let’s look at some exercises to help us understand better.

How many square meters $m²$ are $50,000cm²$?

First, let's recall the exercise we solved previously:

$1m² = 10,000cm²$

Now we can calculate:

$\frac{50,000cm²}{10,000cm²} = 5$

That means,

$1m² = 10,000cm²$

$50,000cm²$ are $5m²$

Given a rectangle that measures $2$ m by $3m$. What is the area of the rectangle in $\text{cm}²$? Calculate it in two different ways.

Let's remember that the formula to calculate the area of a rectangle is base $\times$ height.

Solution:

Method A:

Let's draw the rectangle

Let's calculate the area of the rectangle in $m²$:

$A=2m\times3~m=6~m^2$

That is, we find that the area of the rectangle is $6~m²$. Only that we have been asked for the area in $cm²$.

Let's remember that

$1~m^2=10,000\text{cm}^2$

That is,

$6~m^2=6\times10,000\text{cm}^2=60,000\text{cm}^2$

Therefore, the area of the rectangle expressed in $\text{cm}²$ is $60,000~cm²$

Method B:

Let's draw the rectangle:

In this case, we'll convert the units of measure to $\text{cm}$ at this stage. Remember that $1~m=100\text{cm}$.

We'll write this on the rectangle:

Now let's calculate the area by multiplying the base by the height and we'll obtain:

$A=200\text{cm}\times300\text{cm}=60,000~cm^2$

So, once again we find that the area of the rectangle expressed in $\text{cm}²$ is $60,000~cm²$.

If you're interested in this article, you might also find the following articles interesting:

• Units of Length
• Units of Weight
• Units of Time
• Monetary Units
• Units of Volume

On the Tutorela website, you can find a variety of math articles

What is a unit of area?

Area units are those used to measure the area of geometric figures, lands or some two-dimensional objects, that is, those that have two dimensions (length and width).

How many meters does one hectare have?

One Hectare has $10000m^2$

So if we want to know how many square meters are in $7$ hectares, we need to multiply the number of hectares by the number of square meters in one hectare.

Thus $7\times10000m^2=70000m^2$

Therefore, $7$ hectares is equal to $70000m^2$.

What is the unit of area in the International System of Units (SI)?

As we saw in this article, there are many area measurements, such as:

$\operatorname{km}^2$,$hm^2$,$dam^2$,$m^2$,$cm^2$,$dm^2$ among others, but in the SI, the unit used is the $m^2$