How To Find The Area Of A Rectangle Example

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

What is a Rectangle?

Before finding the expanse of a rectangle, make certain you really take a rectangle. By definition, a rectangle is a 4-sided shape whose angles are all right angles measuring 90 degrees.

You can recognize a rectangle past checking for its ii identifying properties:

Iv interior right angles
2 pairs of parallel, congruent sides

The simply manner 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 (information technology is a plane figure, a quadrilateral with an interior and outside). If everything checks out, see if information technology has four interior angles each of ninety° with opposite, parallel coinciding sides.

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

$Area of a Rectangle$

Area Of A Rectangle

The area is the amount of apartment space inside a rectangle or airtight shape. It is e'er expressed in square units of the linear measurement. And 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.

Surface area is never a linear measure out.

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

$inches (in) = s q u a r e i n c h east s, s q . i north ., i {northward}^{2}$
$feet (ft) = s q u a r due east f eastward due east t, s q . f t ., f t^{2}$
$millimeters (mm) = s q u a r e thou m, m {grand}^{2}$
$centimeters (cm) = s q u a r e c m, c m^{2}$
$meters (m) = s q u a r e m e t east r due south, m^{ii}$

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

Surface area of a Rectangle Formula

The formula for the expanse of a rectangle is:

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

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

How to Observe the Surface area of a Rectangle

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

$How to Find Area of a Rectangle$

Equation For Expanse of a Rectangle

$a r east a = l e northward g t h \times w i d t h$

The floor and rug area is:

$a r e a = iv m \times 3 k$

$a r e a = 12 m^{two}$

How To Solve Expanse of a Rectangle

This side by side example is an extremely common, practical utilise for finding expanse of rectangles. Suppose you are repainting the walls of your bedroom. Ignoring spaces for windows, closet doors and the bedchamber door (yous always purchase a scrap more paint than you will need anyway!), here are the wall dimensions:

Due north wall: 8' tall and 9' broad

Due east wall: 8' tall and 12' wide

South wall: viii' tall and nine' wide

West wall: 8' tall and 12' wide

$How to Find Area of a Rectangle$

Notice all the walls are the aforementioned summit. As well notice the northward and south walls are the aforementioned width, and the east and west walls are the same width. You know your bedchamber is a rectangle. Now let's calculate area:

Due north wall: $viii' \times 9' = 72 f t^{2}$

East wall: $viii' \times 12' = 96 f t^{ii}$

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

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

You can chop-chop add those upwardly to notice your room needs 336 square feet of pigment coverage. A typical gallon of paint covers 400 square feet, so you volition need one gallon of pigment.

How To Calculate Area of a Rectangle

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

$Area of a Rectangle$

$a r e a = 50 east n g t h \times w i d t h$

$a r e a = 54 " \times 36 "$

$a r e a = 1944 i n^{two}$

Surface area of a Rectangle Examples

Case #ii

Say y'all desire a new welcome mat for exterior your dwelling house's front door. You run into one measuring 75 centimeters (cm) long and twoscore cm wide. What is the area of the door mat?

$Area of a Rectangle$

$a r e a = 50 eastward n g t h \times westward i d t h$

$a r e a = 75 c grand \times 40 c grand$

$a r eastward a = 3,000 c m^{2}$

Example #3

Area is oftentimes connected to pricing. Rug is sold in square yards or square meters. Flooring tiles are sold by the square foot. Fifty-fifty things similar new edifice construction and rental properties are calculated as costs per square foot or square meter.

Knowing how to find the area of a rectangle tin can help you observe bargains and avoid wasting money. Let'due south try ane like that. You have two surface area rugs:

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

$Area of a Rectangle Example$

Which gives you the lower cost per foursquare foot? Kickoff, summate the areas of each carpet:

$a r e a = fifty e northward chiliad t h \times westward i d t h$

$a r e a o f b l u east r u g = 6' \times 9' = 54 f t^{ii}$

$a r e a o f b r o w n r u 1000 = 9' \times 12' = 108 f t^{two}$

Now dissever the cost of each rug past its square feet:

$b l u e r u g = \frac{$ 162}{54 f t^{2}} = $ 3 p eastward r f t^{2}$

$b r o w north r u m = \frac{$ 243}{108 f t^{2}} = $ 2.25 p e r f t^{two}$

The brown rug costs less per foursquare foot. Knowing how to find the surface area of a rectangle helped you lot save coin!

$Area of a Rectangle$

Lesson Summary

Past watching the video and reading this lesson, you lot take learned how to recognize a rectangle, what square units are in connectedness with expanse, how to calculate the surface area of a rectangle, and how this skill can exist useful. The formula for calculating the area of a rectangle is length times width, in square units.