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

The function of surface area units is to quantify or measure the area of objects. Since these are two-dimensional units, they are always expressed in square powers. For example, square centimeter $\left(\operatorname{cm}^2\right)$, square meter $\left(m^2\right)$, square kilometer $\left(\operatorname{km}^2\right)$, and so on.

Let's analyze a simple exercise:

We have a rectangle that is $10$ cm long and $7$ cm wide, and we need to calculate its surface area.

In this case, the calculation is quite simple. We will calculate the surface area of the rectangle by multiplying the length by the width, that is, $10cm$ times $7cm$. The result is $70cm^2$. It's crucial to emphasize that since we multiply cm by cm, the result is given in $cm^2$, meaning cm squared(cm raised to the second power).

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

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 theTutorela website, you can find a variety of math articles

Examples and exercises with solutions for surface area units or area measurements

Exercise #1

$8km^2=?m^2$

Video Solution

Step-by-Step Solution

It's important to remember that in one kilometer there are 1000 meters.

Therefore, if there are 8 kilometers, it means there are 8*1000 meters -

8000 meters.

Answer

$8000m^2$

Exercise #2

$5cm=?mm$

Video Solution

Answer

$50$

Exercise #3

$7m=?cm$

Video Solution

Answer

$700$

Exercise #4

$5000cm=?km$

Video Solution

Answer

$0.005$

Exercise #5

$5cm=?mm$

Video Solution

Answer

$50$

Review Questions

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 $m^2$