Area Ratio with the Circumscribed Rectangle

Area Ratio with the Circumscribed Rectangle

The rectangle with sides $$2a$$ and $$2b$$ has area:

$$A_R=4ab$$

Hence the ratio of ellipse area to rectangle area is:

$$\frac{A}{A_R}=\frac{\pi}{4}$$

Usage

- Used in area-ratio problems involving an ellipse and its bounding rectangle.