Area Units or Area Measurements

Every two-dimensional object has an area - the amount of space it covers . For example, every square, rectangle or circle has an area.

Area units are used to measure and express how much space a shape covers. Since area involves two dimensions (length and width), area units are always expressed as squared units. 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 area.

In this case, the calculation is quite simple. We will calculate the 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: area measurements are always expressed in squared units!

Now let's see how to convert between different area units. We'll calculate the area of a square with sides of $1\text{m}$, and express it in both square meters and square centimeters.

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 in centimeters:

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.

Imperial and US Customary Area Units

While the metric system is used in most countries worldwide, the United States and a few other countries use imperial or US customary units for measuring area. Understanding these units is important for practical applications in construction, real estate, land measurement, and everyday life in these regions.

Common Imperial/US Area Units

The most commonly used imperial area units are:

• Square inch $\text{in}^2$ - Used for small areas like paper, screens, or tiles
• Square foot $\text{ft}^2$ - Used for room sizes, apartments, and small plots
• Square yard $\text{yd}^2$ - Used for carpeting, fabric, and medium-sized areas
• Acre $\text{ac}$ - Used for land parcels, farms, and large properties
• Square mile $\text{mi}^2$ - Used for cities, counties, states, and large geographic areas

Understanding the Relationships

Just like metric units, imperial area units follow mathematical relationships based on their linear counterparts:

• $1\text{ ft} = 12\text{ in}$, so $1\text{ ft}^2 = 12\times12 = 144\text{ in}^2$
• $1\text{ yd} = 3\text{ ft}$, so $1\text{ yd}^2 = 3\times3 = 9\text{ ft}^2$
• $1\text{ mile} = 5,280\text{ ft}$, so $1\text{ mi}^2 = 5,280\times5,280 = 27,878,400\text{ ft}^2$

The Acre: A Special Unit

The acre is unique because it doesn't follow the simple pattern above. It's a traditional unit historically defined as the amount of land a yoke of oxen could plow in one day.

• $1\text{ acre} = 43,560\text{ ft}^2$
• $1\text{ acre} = 4,840\text{ yd}^2$
• $640\text{ acres} = 1\text{ mi}^2$

Example 1: Converting Square Feet to Square Inches

Let's say we have a rectangular tablet screen that measures $2\text{ ft}$ long and $1.5\text{ ft}$ wide. What is its area in square inches?

Method A: Calculate in feet first, then convert

Area in square feet: $A = 2\text{ ft} \times 1.5\text{ ft} = 3\text{ ft}^2$

Convert to square inches using $1\text{ ft}^2 = 144\text{ in}^2$: $3\text{ ft}^2 \times 144 = 432\text{ in}^2$

Method B: Convert to inches first, then calculate

Convert dimensions:

• $2\text{ ft} = 2\times12 = 24\text{ in}$
• $1.5\text{ ft} = 1.5\times12 = 18\text{ in}$

Calculate area: $A = 24\text{ in} \times 18\text{ in} = 432\text{ in}^2$

Both methods give us the same result: $432\text{ in}^2$

Example 2: Understanding Acres

A rectangular plot of land measures $300\text{ ft}$ by $145.2\text{ ft}$. How many acres is this?

First, calculate the area in square feet: $A = 300\text{ ft} \times 145.2\text{ ft} = 43,560\text{ ft}^2$

Convert to acres using $1\text{ acre} = 43,560\text{ ft}^2$: $43,560\text{ ft}^2 \div 43,560 = 1\text{ acre}$

This plot is exactly $1\text{ acre}$.

Example 3: Mixed Unit Conversion

A carpet measures $15\text{ ft}$ by $12\text{ ft}$. How many square yards of carpet is this?

Calculate the area in square feet: $A = 15\text{ ft} \times 12\text{ ft} = 180\text{ ft}^2$

Convert to square yards using $1\text{ yd}^2 = 9\text{ ft}^2$: $180\text{ ft}^2 \div 9 = 20\text{ yd}^2$

The carpet covers $20\text{ yd}^2$.

Real-World Applications

• Real Estate: Houses and apartments are typically listed in square feet
• Flooring and Carpeting: Often sold by the square yard or square foot
• Land Sales: Agricultural land and large plots are measured in acres
• Geographic Areas: Countries, states, and cities use square miles
• Construction: Building materials like tiles, shingles, and siding are calculated in square feet or square inches

Converting Between Imperial and Metric

When working internationally or with technical specifications, you may need to convert between imperial and metric units:

• $1\text{ in}^2 \approx 6.452\text{ cm}^2$
• $1\text{ ft}^2 \approx 0.093\text{ m}^2$
• $1\text{ acre} \approx 0.405\text{ ha}$ or $\approx 4,047\text{ m}^2$
• $1\text{ mi}^2 \approx 2.590\text{ km}^2$

These conversions are approximate because imperial and metric systems are based on different standards.

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

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 $2m$ 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 length $\times$ width (or 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 $m^2$