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### Area of an Ellipse

```
Date: 08/18/99 at 09:50:02
From: Tom Turlais
Subject: Area of an ellipse

I am a mentor of junior and senior high school students at a local
learning center. The question has arisen:

How do you calculate the area of an ellipse?

Will you help with this?
```

```
Date: 08/18/99 at 12:27:58
From: Doctor Peterson
Subject: Re: Area of an ellipse

Hi, Tom.

We have a FAQ on geometrical formulas here, which may be useful:

http://mathforum.org/dr.math/faq/formulas/

The area of an ellipse is very simple:

A = pi a b

where a and b are the semiaxes (the "radii" in each direction.) It's
just the familiar "pi r squared" with each "r" replaced by one of the
axes.

This is because an ellipse is just a circle "stretched" in one
direction, so the area is just that of the circle you start with, say
with radius a, times the ratio by which you stretched it, b/a:

A = pi a^2 * b/a = pi a b

*****
***  |  ***
**     |     **
*       |       *
*        |        *
*     ...b|....     *
*   ...    |    ...   *
* ..       |       .. *
*.         |a        .*
*.          |          .*
.           |           .
.           +-----------.
.                 a     .
*.                     .*
*.                   .*
* ..               .. *
*   ...         ...   *
*     .........     *
*                 *
*               *
**           **
***     ***
*****

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry

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