How to Find the Area of an Ellipse
Question
An ellipse is a(n)
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How to Find the Area of an Ellipse

Hi, I am Eric Stone from South Burlington High School in South Burlington, Vermont, here for About.com. Today, we are going to talk about the area of an ellipse.The first thing we need to do is define what an ellipse is. Well, an ellipse is an oblong circle, almost like an egg, but not quite because an egg is fatter on one end than it is on the other side. Instead, it has got one side that is longer than the other -- it is almost a circle. And you can imagine you can lengthen it or shorten it however you wish.It has two very important properties. One is this thing we call the major axis. The major axis is the long side of an ellipse and it is usually defined as 2a -- a being the distance from the center of an ellipse out to the edge on that long axis, or major axis. In the other direction, we have the width of the ellipse, which in this case is going to be defined as 2b -- where b is the distance from the center of the ellipse out to the edge.
This is really important, because sometimes the problem will be defined in terms of just the length and width of the ellipse, and sometimes it will be defined as a or b.So imagine we have a sticker company and we want to know how much sticker material will we need to produce 1,000 stickers. Well if they're those cool euro-stickers you see on the back of the car, where 4 inches is the length and 3 inches is the height you want -- and you want to produce 1,000 of those -- how much sticker material will I need?
No problem. I use the formula for the area of an ellipse, which is simply area equals pi times a times b. Remember, a is defined as the distance from the center out to the edge on the major axis, and b is the distance from the center out to edge along the minor axis.So if I want to find the area of an ellipse, all I need to do is redefine my 4 inches in length to be 2 inches for a. Take my 3 inches, which was my width of my sticker, and redefine it to be 1.5 inches -- which will be my b. Multiply, and the area is going to be equal to 3-pi. 3-pi is approximately 9.5 square inches, so if I want to order 1,000 of these stickers, I'm going to need 9.5 square inches times a thousand, or 9,500 square inches of sticker material.
And that is how you find the area of an ellipse. Thanks for watching! To learn more, visit us on the web at About.com.