Area of a circle = `2pir^(2)` .

Answer

To solve the question regarding the area of a circle, we need to clarify the formula provided in the question.

### Step-by-Step Solution:

1. **Understand the Question**: The question states that the area of a circle is equal to \(2\pi r^2\). We need to verify if this statement is true or false.

2. **Recall the Correct Formula**: The standard formula for the area \(A\) of a circle is given by:
\[ A = \pi r^2 \]
where \(r\) is the radius of the circle.

3. **Compare the Given Formula with the Correct Formula**: The formula given in the question is \(2\pi r^2\). We need to compare this with the correct formula:
- Given: \(2\pi r^2\)
- Correct: \(\pi r^2\)

4. **Conclusion**: Since \(2\pi r^2\) is not equal to \(\pi r^2\), we conclude that the statement in the question is false. The area of a circle is not \(2\pi r^2\); it is \(\pi r^2\).

### Final Answer:
The area of a circle is not equal to \(2\pi r^2\); it is actually \(\pi r^2\).

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