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To determine the area of the triangle \( \triangle OPQ \), we need to follow these steps:

1. **Identify the coordinates of points \( P \) and \( Q \) on the graph of \( f(x) = \frac{1}{x} \):**
   - \( P = (a, f(a)) = \left(a, \frac{1}{a}\right) \)
   - \( Q = \left(\frac{1}{a}, f\left(\frac{1}{a}\right)\right) = \left(\frac{1}{a}, a\right) \)

2. **Calculate the vertices of the triangle:**
   - \( O = (0, 0) \)
   - \( P = \left(a, \frac{1}{a}\right) \)
   - \( Q = \left(\frac{1}{a}, a\right) \)

3. **Use the determinant formula for the area of a triangle given its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):**
   \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

4. **Substitute the coordinates of \( O \), \( P \), and \( Q \):**
   \[ \text{Area} = \frac{1}{2} \left| 0 \left(\frac{1}{a} - a\right) + a \left(a - 0\right) + \frac{1}{a} \left(0 - \frac{1}{a}\right) \right| \]

5. **Simplify the expression:**
   \[ \text{Area} = \frac{1}{2} \left| 0 + a^2 + \frac{1}{a} \left(-\frac{1}{a}\right) \right| \]
   \[ \text{Area} = \frac{1}{2} \left| a^2 - \frac{1}{a^2} \right| \]

6. **Final area calculation:**
   \[ \text{Area} = \frac{1}{2} \left| a^2 - \frac{1}{a^2} \right| \]

### Answer:
The area of the triangle \( \triangle OPQ \) in terms of \( a \) is:
\[ \boxed{\frac{1}{2} \left| a^2 - \frac{1}{a^2} \right|} \]

If you have any further questions or need more details, feel free to ask! Here are some questions you might be interested in:

1. How can I verify the coordinates of points \( P \) and \( Q \)?
2. Can you provide a detailed explanation of the determinant formula used for the area of a triangle?
3. What if the function \( f(x) \) was different, how would that affect the area calculation?
4. Can you provide a graph for better visualization?
5. Are there alternative methods to solve this problem?

**Tip:** Always ensure the correct interpretation of the function and its points when solving geometry problems involving areas of triangles.

Learn how to calculate the area of triangle OPQ using coordinate geometry and the determinant formula. This problem involves identifying triangle vertices, applying the determinant formula, and simplifying expressions. Suitable for high school students studying coordinate geometry.

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