Surface Area Units or Area Measurements

🏆Practice area units

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 (cm2) \left(\operatorname{cm}^2\right) , square meter (m2) \left(m^2\right) , square kilometer (km2) \left(\operatorname{km}^2\right) , and so on.

Let's analyze a simple exercise:

We have a rectangle that is 10 10 cm long and 7 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 10cm times 7cm 7cm . The result is 70cm2 70cm^2 . It's crucial to emphasize that since we multiply cm by cm, the result is given in cm2 cm^2 , meaning cm squared(cm raised to the second power).

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\( 291cm^2=?m^2 \)

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Surface Area Measures:

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

Examples of Surface Area Measurements

cm2 \text{cm}^2 (square centimeter), m2 m^2 (square meter), km2 \text{km}^2 (square kilometer).

These units are different, but they are related:

1km2=1,000,000m2 1\text{km}^2=1,000,000\text{m}^2

1m2=10,000cm2 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 cm2 \text{cm}^2 are in 1m2 1\text{m}^2 . We’ll draw a square whose sides each measure 1 1 meter:

Image of a 1 m^2 square

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 =1m×1m =1\text{m}\times1\text{m} .

The result is 11 m² or, writing it another way:

S=1m2 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 cm \text{cm} .

That is:

image of a 100cm^2 square

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

The area of the square =100cm×100cm=10,000cm2 =100\text{cm}\times100\text{cm}=10,000\text{cm}^2

Or, writing it another way:

S=100cm×100cm=10,000cm2 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 1 square meter, and the second time the same area is equivalent to 10,000cm2 10,000\text{cm}^2 .

We can deduce that:

1m2=10,000cm2 1\text{m}^2=10,000\text{cm}^2

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

1m2=1m×1m=100cm×100cm=10,000cm2 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.

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Exercise 1

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

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

1m2=10,000cm2 1m² = 10,000cm²

Now we can calculate:

50,000cm210,000cm2=5 \frac{50,000cm²}{10,000cm²} = 5

That means,

1m2=10,000cm2 1m² = 10,000cm²

50,000cm2 50,000cm² are 5m2 5m²

Exercise 2

Given a rectangle that measures 2 2 m by 3m 3m . What is the area of the rectangle in cm2 \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.


Method A:

Let's draw the rectangle

image of a 2m by 3m rectangle

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

A=2m×3 m=6 m2 A=2m\times3~m=6~m^2

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

Let's remember that

1 m2=10,000cm2 1~m^2=10,000\text{cm}^2

That is,

6 m2=6×10,000cm2=60,000cm2 6~m^2=6\times10,000\text{cm}^2=60,000\text{cm}^2

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

Method B:

Let's draw the rectangle:

image of a 2m by 3m rectangle

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

We'll write this on the rectangle:

image of a rectangle of 200cm by 300 cm

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

A=200cm×300cm=60,000 cm2 A=200\text{cm}\times300\text{cm}=60,000~cm^2

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

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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 10000m2 10000m^2

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

Thus 7×10000m2=70000m2 7\times10000m^2=70000m^2

Therefore, 7 7 hectares is equal to 70000m2 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:

km2 \operatorname{km}^2 ,hm2 hm^2 ,dam2 dam^2 ,m2 m^2 ,cm2 cm^2 ,dm2 dm^2 among others, but in the SI, the unit used is the m2 m^2

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