The area of the region bounded by the ellipse `(x^(2))/25+y^(2)/16=1` is

Options

A. `20pi" sq units"`
B. `20pi^(2)" sq units"`
C. `16pi^(2)" sq units"`
D. `25 pi " sq units"`

Explanation

To find the area of the region bounded by the ellipse given by the equation \(\frac{x^2}{25} + \frac{y^2}{16} = 1\), we can follow these steps:

### Step 1: Identify the semi-major and semi-minor axes
The equation of the ellipse can be rewritten in the standard form:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
where \(a^2 = 25\) and \(b^2 = 16\). Thus, we have:
\[ a = 5 \quad \text{and} \quad b = 4 \]

### Step 2: Use the formula for the area of an ellipse
The area \(A\) of an ellipse is given by the formula:
\[ A = \pi \cdot a \cdot b \]
Substituting the values of \(a\) and \(b\):
\[ A = \pi \cdot 5 \cdot 4 \]

### Step 3: Calculate the area
Now, we calculate the area:
\[ A = 20\pi \]

### Conclusion
Thus, the area of the region bounded by the ellipse is:
\[ \boxed{20\pi} \]

---