# Surface Area Units or Area Measurements

🏆Practice area units

## Surface Area Measures

$\text{cm}^2$ (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:

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

## Test yourself on area units!

$$8km^2=?m^2$$

## Surface Area Measures

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 simplock-key="b5mc7">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 [object Object][object Object] cm by cm, the result is given [object Object], meaning cm a>(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 $=100\text{cm}\times100\text{cm}=10,000\text{cm}^2$

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.

### Exercise 1

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 $5m²$

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### Exercise 2

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

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

### Exercise #1

$8km^2=?m^2$

### Video Solution

$8000m^2$

### Exercise #2

$5cm=?mm$

### Video Solution

$50$

### Exercise #3

$7m=?cm$

### Video Solution

$700$

### Exercise #4

$5000cm=?km$

### Video Solution

$0.005$

### Exercise #5

$5cm=?mm$

### Video Solution

$50$

## 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 $m^2$

Do you know what the answer is?