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### Heron's Formula

```Date: 04/11/2003 at 08:41:02
From: Lesley
Subject: Area of Triangles

Dear Dr. Math,

How can I find the area of an isosceles triangle, an equilateral
triangle, a scalene triangle, an obtuse-angle triangle and an acute-
angle triangle without the height being given?

Lesley
```

```
Date: 04/11/2003 at 12:03:43
From: Doctor Rick
Subject: Re: Area of Triangles

Hi, Lesley.

You forgot to tell me what IS given!

If you know the lengths of the three sides of a triangle, there is a
formula called Heron's formula. I did not learn it when I was your
age, as far as I can remember; it's more complicated than half the
base times the height. First you calculate something called the semi-
perimeter, s. As the name says, it's half the perimeter, that is,
half the sum of the lengths of the sides:

s = (a+b+c)/2   where a, b, c are the lengths of the sides

Then you multiply this number by three other numbers - the semi-
perimeter minus each of the three sides in turn - and take the square
root of the result:

A = sqrt(s(s-a)(s-b)(s-c))

That's the area of the triangle.

Is this what you're looking for?

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 04/11/2003 at 22:45:30
From: Lesley
Subject: Thank you (Area of Triangles)

Yup, that's the one. Thanks Dr. Math!

Lesley
```
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

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