A ratio can help you find the area of any circle or ellipse. Because all circles are similar, the ratio of a circle to a square that is the same distance across has a specific value. And because an ellipse is essentially a stretched circle, the same ratio can help you find the area of an ellipse. Discuss this idea with students by showing them the diagrams below.
Ask students these questions to help discover and use a ratio.
- What is the area of the circle? [Pi * 1 * 1 = Pi or about 3.14]
- What is the area of the square? [4 units]
- What is the ratio of the area of the circle to the area of the square? [Pi/4 or about .785]
- If you know the diameter of any circle, how can you find the area? [Square the diameter and multiply by .785]
- What is the area of the rectangle? [L x W = 12[
- What is the ratio of the area of the ellipse to the area of the rectangle? [0.785]
- What is the area of the ellipse? [9.42]
- Another formula for the area of an ellipse involves multiplying pi times half the length times half the width. Why is this equivalent? [L/2 times W/2 times Pi can be simplified to .785LW]