How would you find an oval with the same area of a circle?

Answer 1

An oval is a general word that could have different shapes. If you squash a circle evenly, the new shape in math is called an ellipse, which has an oval shape.

The formula for the area of a circle is Pi times the Radius of the circle squared. The radius is half the height of the circle and also half the width of the circle.

The general formula for the area of an ellipse is Pi times half the height times half the width. So we say length A is half the height of an ellipse and length B is half the width of an ellipse. When A is equal to B you have a circle. When they are different you have an ellipse.

So if you want the area of the circle to be the same as the area of the ellipse, then you have to keep the height times the width the same for the ellipse as it was for the circle. As you squash the ellipse further the width must stretch out more than the height gets pushed down.

For example, a circle with radius of 1 inch would have the same area as an ellipse with height ½ inch and width 2 inches because 1 times 1 is equal to ½ times 2. Another ellipse with the same area could have height ¼ inch and width 4 inches.