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/