How To Find the Area of a Rectangle
What is a rectangle?
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.
Area of a rectangle
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:
inches (in) = square in,
feet (ft) = square ft,
millimeters (mm) = square mm,
centimeters (cm) = square cm,
meters (m) = square m,
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.
Area of a rectangle formula
The formula for the area of a rectangle is:
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.
How to find the area of a rectangle
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.
Equation for area of a rectangle
The floor and carpet area is:
How to solve area of a rectangle
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' × 9' =
East wall: 8' × 12' =
South wall: 8' × 9' =
West wall: 8' × 12' =
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.
How to calculate area of a rectangle
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 of a rectangle examples
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?
Example #3
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:
Now divide the cost of each rug by its square feet:
The brown rug costs less per square foot. Knowing how to find the area of a rectangle helped you save money!
Lesson summary
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.