- What is a Rectangle?
- Area Of A Rectangle
- Area of a Rectangle Formula
- How to Find the Area of a Rectangle
- How To Calculate Area of a Rectangle
- Area of a Rectangle Examples

Before finding the area of a rectangle, make sure you actually *have* a rectangle. By definition, a **rectangle** is a four-sided shape whose angles are all right angles measuring 90 degrees.

You can recognize a rectangle by checking for its two **identifying properties**:

- Four interior right angles
- Two pairs of parallel, congruent sides

The only way to construct a polygon meeting those two requirements is to make a rectangle. So check to see if you have a flat, closed, four-sided shape (it is a plane figure, a quadrilateral with an interior and exterior). If everything checks out, see if it has four interior angles each of 90° with opposite, parallel congruent sides.

If your shape has all those qualities, you have a rectangle and you can find its area.

The area is the amount of flat space inside a rectangle or closed shape. It is always expressed in square units of the linear measurement. So, if a shape is 11 yards long and 7 yards wide, its area is expressed in square yards, even though the shape is not a square.

Area is never a linear measure.

A square unit of anything is one unit of length times one unit of width. Here are some common linear measurements, their square units, and the ways to write and abbreviate them:

- $\mathbf{inches}\mathbf{(}\mathbf{in)}=squareinches,sq.in.,i{n}^{2}$
- $\mathbf{feet}\mathbf{(}\mathbf{ft)}=squarefeet,sq.ft.,f{t}^{2}$
- $\mathbf{millimeters}\mathbf{(}\mathbf{mm)}=squaremm,m{m}^{2}$
- $\mathbf{centimeters}\mathbf{(}\mathbf{cm)}=squarecm,c{m}^{2}$
- $\mathbf{meters}\mathbf{(}\mathbf{m)}=squaremeters,{m}^{2}$

Each time, you simply take the unit of linear measure and multiply it times itself (square it). You do this because you are trying to understand how much closed space, the shape contains.

The **formula** for the area of a rectangle is:

$area=length\times width$

If you do not know what the length of a rectangle is, though, that formula will not do you much good. So make certain you can identify the two linear measurements of the rectangle.

The length of any polygon is always understood to be its larger dimension, even when its length is not presented horizontally.

Imagine you are installing a new wall-to-wall carpet in a room. This is a very common use for finding area. The room is 4 meters long and 3 meters wide. To reach to all four corners (wall-to-wall), your carpet must also be 4 meters long and 3 meters wide.

$area=length\times width$

The floor and carpet area is:

$area=4m\times 3m$

$area=12{m}^{2}$

This next example is an extremely common, practical use for finding area of rectangles. Suppose you are repainting the walls of your bedroom. Ignoring spaces for windows, closet doors and the bedroom door (you always buy a bit more paint than you will need anyway!), here are the wall dimensions:

North wall: 8' tall and 9' wide

East wall: 8' tall and 12' wide

South wall: 8' tall and 9' wide

West wall: 8' tall and 12' wide

Notice all the walls are the same height. Also notice the north and south walls are the same width, and the east and west walls are the same width. You know your bedroom is a rectangle. Now let's calculate area:

North wall: $8\text{'}\times 9\text{'}=72f{t}^{2}$

East wall: $8\text{'}\times 12\text{'}=96f{t}^{2}$

South wall: $8\text{'}\times 9\text{'}=72f{t}^{2}$

West wall: $8\text{'}\times 12\text{'}=96f{t}^{2}$

You can quickly add those up to discover your room needs 336 square feet of paint coverage. A typical gallon of paint covers 400 square feet, so you will need one gallon of paint.

Suppose you need a soft blanket for your dog's daytime kennel. The kennel floor measures 54 inches long and 36 inches wide. What is the area of the blanket you need?

$area=length\times width$

$area=54"\times 36"$

$area=1944i{n}^{2}$

Say you want a new welcome mat for outside your home's front door. You see one measuring 75 centimeters (cm) long and 40 cm wide. What is the area of the door mat?

$area=length\times width$

$area=75cm\times 40cm$

$area=\mathrm{3,000}c{m}^{2}$

Area is often connected to pricing. Carpet is sold in square yards or square meters. Floor tiles are sold by the square foot. Even things like new building construction and rental properties are calculated as costs per square foot or square meter.

Knowing how to find the area of a rectangle can help you find bargains and avoid wasting money. Let's try one like that. You have two area rugs:

- Blue rug: 6' x 9' for $162
- Brown rug: 9' x 12' for $243

Which gives you the lower cost per square foot? First, calculate the areas of each rug:

$area=length\times width$

$areaofbluerug=6\text{'}\times 9\text{'}=54f{t}^{2}$

$areaofbrownrug=9\text{'}\times 12\text{'}=108f{t}^{2}$

Now divide the cost of each rug by its square feet:

$bluerug=\frac{\$162}{54f{t}^{2}}=\$3perf{t}^{2}$

$brownrug=\frac{\$243}{108f{t}^{2}}=\$2.25perf{t}^{2}$

The brown rug costs less per square foot. Knowing how to find the area of a rectangle helped you save money!

By watching the video and reading this lesson, you have learned how to recognize a rectangle, what square units are in connection with area, how to calculate the area of a rectangle, and how this skill can be useful. The formula for calculating the area of a rectangle is length times width, in square units.

After reading this lesson and viewing the video, you will learn to:

- Recognize a rectangle
- Understand square units and area
- Calculate the area of a rectangle
- Connect this skill to real-life situations where the skill is useful

Instructor: **Malcolm M.**

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.

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