Heading: Finding the Area of the Region Bounded by the Ellipse

To find the area of the region bounded by an ellipse, we can use the formula for the area of an ellipse:

A = π * a * b

where "a" and "b" are the lengths of the major and minor axes of the ellipse, respectively.

Explanation:

1. Identify the lengths of the major and minor axes:
- The major axis is the longest diameter of the ellipse, which passes through the center and is perpendicular to the minor axis.
- The minor axis is the shortest diameter of the ellipse, which passes through the center and is perpendicular to the major axis.
- Measure or determine the lengths of the major and minor axes of the ellipse.

2. Calculate the values of "a" and "b":
- Let "a" be the length of the major axis and "b" be the length of the minor axis.
- Substitute the values of "a" and "b" into the formula A = π * a * b.

3. Evaluate the formula:
- Multiply the values of π, "a", and "b" together.
- This will give you the area of the ellipse.

4. Write the final answer:
- State the area of the region bounded by the ellipse, using appropriate units of measurement.

Example:

Suppose we have an ellipse with a major axis of length 8 units and a minor axis of length 4 units.

1. Identify the lengths of the major and minor axes:
- Major axis: 8 units
- Minor axis: 4 units

2. Calculate the values of "a" and "b":
- a = 8 units
- b = 4 units

3. Evaluate the formula:
- A = π * a * b = 3.1416 * 8 * 4 = 100.5316 square units

4. Write the final answer:
- The area of the region bounded by the ellipse is approximately 100.5316 square units.

Conclusion:

The area of the region bounded by an ellipse can be found using the formula A = π * a * b, where "a" and "b" are the lengths of the major and minor axes, respectively. By substituting the values into the formula, we can calculate the area of the ellipse.