Area of an Eclipse
Formula: πab
The circle and the eclipse are similar, except the eclipse is warped. A circle's radius will have the same length no matter where it lands on the edge of the shape, however, an eclipse's radius has 2 different lengths classified as "a" and "b". By multiplying these two lengths together and with the digit pi, you are able to find the total area of the eclipse.
Examples
A practical example of using the area of an ellipse in the real world is in landscaping, particularly when designing an elliptical flower bed or lawn area.
Suppose you have an elliptical garden plot and want to determine how much grass seed or mulch to buy. To find the area, you need the lengths of the major axis (the longest diameter) and the minor axis (the shortest diameter). Let's say the major axis is 10 meters and the minor axis is 6 meters. The formula for the area of an ellipse is:
Area=π×semi-major axis×semi-minor axis
First, calculate the semi-major and semi-minor axes:
semi-major axis=major axis/2=10meters/2= 5meters
semi-minor axis=minor axis/2 =6meters/2 =3meters
Area=π×5meters×3meters
Area=π×15square meters
Area≈3.14×15
Area≈47.1square meters
By calculating the area, you determine that the elliptical garden plot is approximately 47.1 square meters. This helps you purchase the right amount of grass seed, mulch, or other materials to cover the entire area properly.
