# How to Measure Four-Sided Shapes

Two important skills in geometry — and real life — are finding the perimeter and calculating the area of shapes. A shape’s *perimeter* is a measurement of the length of its sides. You use perimeter for measuring the distance around the edges of a room, building, or circular pathway. A shape’s *area* is a measurement of how big it is inside.

## Measuring squares

The letter *s* represents the length of a square’s side. For example, if the side of a square is 3 inches, then you say *s* = 3 in. Finding the perimeter *(P)* of a square is simple: Just multiply the length of the side by 4. Here’s the formula for the perimeter of a square:

For example, if the length of the side is 3 inches, substitute 3 inches for *s* in the formula:

Finding the area of a square is also easy: Just multiply the length of the side by itself — that is, take the *square* of the side. Here are two ways of writing the formula for the area of a square (*s*^{2} is pronounced “s squared”):

For example, if the length of the side is 3 inches, then you get the following:

## Working with rectangles

The long side of a rectangle is called the *length*, or *l* for short. The short side is called the *width*, or *w* for short. For example, in a rectangle whose sides are 5 and 4 feet long, *l* = 5 ft. and *w* = 4 ft.

Because a rectangle has two lengths and two widths, you can use the following formula for the perimeter of a rectangle:

Calculate the perimeter of a rectangle whose length is 5 yards and whose width is 4 yards as follows:

The formula for the area of a rectangle is:

So here’s how you calculate the area of the same rectangle:

## Calculating with rhombuses

As with a square, use *s* to represent the length of a rhombus’s side. But another key measurement for a rhombus is its height. The *height* of a rhombus (*h* for short) is the shortest distance from one side to the opposite side. Here, *s* = 4 cm and *h* = 2 cm.

The formula for the perimeter of a rhombus is the same as for a square:

Here’s how you figure out the perimeter of a rhombus whose side is 4 centimeters:

To measure the area of a rhombus, you need both the length of the side and the height. Here’s the formula:

So here’s how you determine the area of a rhombus with a side of 4 cm and a height of 2 cm:

You can read 8 cm^{2} as “8 square centimeters” or, less commonly, as “8 centimeters squared.”

## Measuring parallelograms

The top and bottom sides of a parallelogram are called its *bases* (*b* for short), and the remaining two sides are its *sides* *(s)*. And as with rhombuses, another important measurement of a parallelogram is its *height* *(h)*, the shortest distance between the bases. So the parallelogram here has these measurements: *b* = 6 in., *s* = 3 in., and *h* = 2 in.

Each parallelogram has two equal bases and two equal sides. Therefore, here’s the formula for the perimeter of a parallelogram:

To figure out the perimeter of the parallelogram, just substitute the measurements for the bases and sides:

And here’s the formula for the area of a parallelogram:

Here’s how you calculate the area of the same parallelogram:

## Measuring trapezoids

The parallel sides of a trapezoid are called its bases. Because these bases are different lengths, you can call them *b** _{1}* and

*b*

*. The height*

_{2}*(h)*of a trapezoid is the shortest distance between the bases. Thus, the trapezoid here has these measurements:

*b*

*= 2 in.,*

_{1}*b*

*= 3 in., and*

_{2}*h*= 2 in.

Because a trapezoid can have sides of four different lengths, you really don’t have a special formula for finding the perimeter of a trapezoid. Just add up the lengths of its sides, and you get your answer.

Here’s the formula for the area of a trapezoid:

So here’s how to find the area of the pictured trapezoid: