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### Triangle Area

```
Date: 08/13/97 at 21:22:02
From: Anonymous
Subject: Triangle Area

How do you find the area of a triangle?
```

```
Date: 08/19/97 at 08:59:54
From: Doctor Rob
Subject: Re: Triangle Area

That depends on the information you are given. Let S be the area you
want to find. Here are some cases, where first is stated the given
information, then the formula for S:

1. The lengths of one side (or base) b and the altitude h
perpendicular to it.  S = b*h/2.

2. The lengths of two sides a and b, and the measure of the angle C
between them.  S = a*b*sin(C)/2.

3. The lengths of all three sides a, b, and c.  Let s = (a+b+c)/2.
S = Sqrt[s*(s-a)*(s-b)*(s-c)].

4. The measure of two angles A and B, and the length of the side c
between them. S = (c^2/2)*sin(A)*sin(B)/sin(A+B).

Here sin(x) is the sine of angle x.  Many calculators have a button to
calculate the sine function.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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