Area of a Rectangle and/or Square

Area = (l) (w)

Where:
l = length
w = width

The area of a rectangle/square tells how large the rectangle/square is in square units (miles, feet, inches, etc.)

The equation simply consists of multiplying the value of the length (or vertical height) of the shape by its width (horizontal span.)

The area of a rectangle/square must be in square units because when assigning one number for the measurement of a square, both the length and the width need to be accounted for.

By using square units you say how many smaller squares fit into the larger square being measured. So, for example, when I say the area of a rectangle is 150 sq. in. it means that 150 smaller squares with the area of 1 sq in. fit into the total area rectangle. This way, both the length and the width of the square is included in your answer.

Square units are most commonly notated by putting a superscript "²" to the top of the abbreviated unit. So, for example, square inches (square in) would be notated as in² and square feet (square ft) would be notated as ft².

We use the same calculation for finding the area of both squares and rectangles because the only difference between squares and rectangles are the length of their sides. A square's sides are all the same while the length and width of a rectangle always differ. But do note that a rectangle's width of its top line is the same as the width of its bottom line and its length on both sides are also the same.

When is this Formula Used Outside of Math Class?
You will soon find out that this equation is definitely not one of those that you don't know any good use for in the "real world." Architects, construction workers, interior designers, home and property owners, environmentalists or lawn workers who wish to chemically treat ponds or land, textile and fashion designers, web and computer graphic designers, and many others use this formula daily.

Rug Thug
Angie loves rugs and has an abundance of them. She needs to find the area of her new bedroom so she knows how many rugs she can fit in it. She has five rugs she wants to put in her bedroom; one is 30.5 square feet, two are 12 square feet, one is 6 square feet, and another is 5.6 square feet. She measured that her room is 10 feet long and 7.5 feet wide. How many of her rugs can she fit in her bedroom?

First, find the area of her room by plugging its dimensions into our formula:
Area = (l) (w)
Area = (10) (7.5)

Multiply these dimensions together:
(10) (7.5) = 75 square feet/ft²

Her room is 75 square feet. If the total amount square footage of her rugs is under that, she can fit all of them in her room.  If it is over that, she'll have to leave one or two out.

Add all the square footage of each of her rugs together:
30.5 + 12 + 12 + 6 + 5.6
= 30.5 + 24 + 11.6
= 30.5 + 35.6
= 66.1

Angie can fit all of her rugs into her new bedroom, but there will only be about 9 square feet of open floor (75 ft² minus 66.1 ft².) If her rugs don't all match each other, she'll surely have an odd-looking floor.
Note: For those of you who like to think in percentages, only twelve percent (12%) of her floor will be left open. (I found that percentage by dividing the uncovered space in her room by the amount of space total (9 / 75).)

Fair and Square
Since their mom just had a baby, brothers Peter and Timmy have to share a room. They want to avoid fighting over whose space is whose, so they want to split the room evenly in half and each claim one side. The dimensions of their room are 12 feet (length) by 7.4 feet (width.) How much space will each of them have?

First, find the total area of the room they will be sharing by plugging its dimensions into our equation:
Area = (l) (w)
Area = (12) (7.4)

Do the multiplication:
(12 (7.4) = 88.8 ft²
The room is 88.8 ft² total; so they must divide that by two to see how much space they each get:
88.8 / 2 = 44.4

So, they each only get 44.4 ft² to themselves.

Related websites:
http://www.mathgoodies.com/lessons/vol1/area_rectangle.html
http://www.webmath.com/k8rectangle.html
http://illuminations.nctm.org/activitydetail.aspx?id=46

Works Cited

Spiegel, Murray, and John Liu. Mathematical Handbook of Formulas and Tables.
     U.S.A.: McGraw-Hill Companies, Inc., 1999.

"Chemical Treatment of Ponds." Colorado State Cooperative Extension. 9 June 2006.
     Colorado State University. 19 June 2006.
     http://www.ext.colostate.edu/pubs/natres/06400.html