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The equation of the ellipse given is:

\[
\frac{x^2}{4} + \frac{y^2}{9} = 1
\]

This equation is in the standard form of an ellipse:

\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]

where \( a^2 = 4 \) and \( b^2 = 9 \), so:

- \( a = 2 \) (the semi-major axis along the x-axis)
- \( b = 3 \) (the semi-minor axis along the y-axis)

The area \( A \) of an ellipse is given by the formula:

\[
A = \pi \cdot a \cdot b
\]

Substituting the values of \( a \) and \( b \):

\[
A = \pi \cdot 2 \cdot 3 = 6\pi
\]

So, the area of the ellipse is \( 6\pi \).

The correct answer is:

\[
\boxed{6\pi}
\]

Would you like further details or have any questions? Here are five related questions:

1. How do you derive the general formula for the area of an ellipse?
2. What would change in the area formula if the ellipse were rotated?
3. How can you calculate the eccentricity of the given ellipse?
4. What is the relationship between the semi-major and semi-minor axes and the focal distance of an ellipse?
5. How would you find the perimeter of this ellipse, even though it doesn't have a simple formula like the area?

**Tip:** When solving geometry problems involving ellipses, always identify the semi-major and semi-minor axes from the equation first.

Given an ellipse with equation \(\frac{x^2}{4} + \frac{y^2}{9} = 1\), compute the area of the ellipse.

Learn how to compute the area of an ellipse with the given equation x^2/4 + y^2/9 = 1. This problem explains the use of the area formula A = πab, with values of the semi-major and semi-minor axes for the ellipse. Suitable for high school students.

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