Basic Math and Pre-Algebra For Dummies (78 page)

 
The area of a shape is always measured in
square units:
square inches (in.
²
), square feet (ft.
²
), square miles (mi.
²
), square kilometers (km
²
), and so on — even if you're talking about the area of a circle! (For more on measurements, flip to Chapter
15
.)

I cover these types of calculations in this section. (For more information on the names of shapes, refer to “Closed Encounters: Shaping Up Your Understanding of 2-D Shapes.”)

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 (A) 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:

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:

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. In Figure 
16-12
,
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: