Basic Math and Pre-Algebra For Dummies (80 page)

Here's the formula for the area of a triangle:

So here's how to figure out the area of a triangle with a base of 5 cm and a height of 2 cm:

The long side of a right triangle
(c)
is called the
hypotenuse,
and the two short sides (
a
and
b
) are called the
legs
(see Figure 
16-16
). The most important right triangle formula is the
Pythagorean theorem
:

This formula allows you to find the hypotenuse of a triangle, given only the lengths of the legs. For example, suppose the legs of a triangle are 3 and 4 units. Here's how to use the Pythagorean theorem to find the length of the hypotenuse:

So when you multiply
c
by itself, the result is 25. Therefore,

• c
  = 5
  

The length of the hypotenuse is 5 units.

The
center
of a circle is a point that's the same distance from any point on the circle itself. This distance is called the
radius
of the circle, or
r
for short. And any line segment from one point on the circle through the center to another point on the circle is called a
diameter
, or
d
for short. See Figure 
16-17
.

As you can see, the diameter of any circle is made up of one radius plus another radius — that is, two
radii
(pronounced
ray
-dee-eye). This concept gives you the following handy formula:

For example, given a circle with a radius of 5 millimeters, you can figure out the diameter as follows:

Because the circle is an extra-special shape, its perimeter (the length of its “sides”) has an extra-special name: the
circumference
(
C
for short). Early mathematicians went to a lot of trouble figuring out how to measure the circumference of a circle. Here's the formula they hit upon:

Note:
Because 2 ×
r
is the same as the diameter, you also can write the formula as
C
= π ×
d
.

 The symbol π is called
pi
(pronounced “pie”). It's just a number whose approximate value is as follows (the decimal part of pi goes on forever, so you can't get an exact value for pi):

So given a circle with a radius of 5 mm, you can figure out the approximate circumference: