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The image presents a question about the formula for the area of a triangle. The area of a triangle is given by:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Now, let's evaluate the given options to see which correctly represents this formula:

1. **\( A = \frac{x + y}{2} \)**: This formula does not represent the area of a triangle since it uses \( x \) and \( y \) instead of the base and height.
   
2. **\( A = \frac{1}{2} \times (12)(5) \)**: This is a correct formula for the area of a triangle with base 12 and height 5, though specific numbers are plugged in.
   
3. **\( A = \frac{1}{2} \times (b + h) \)**: Incorrect. The area involves multiplying the base and height, not adding them.
   
4. **\( A = \frac{x^2}{2} \)**: This does not match the formula for the area of a triangle, but might represent some other geometric calculation.
   
5. **\( A = \frac{1}{2} \times (b \times h) \)**: This is the correct general formula for the area of a triangle.

Thus, options **2** and **5** correctly represent the formula for the area of a triangle.

Would you like more details or have any questions about this? Here are some related questions:

1. How do you derive the formula for the area of a triangle?
2. Can you explain why the second option with specific numbers is correct?
3. What are some examples of real-world applications of the triangle area formula?
4. How does the formula change for other polygons?
5. What happens to the area if both the base and height are doubled?

**Tip:** The formula for the area of a triangle applies to all triangles, even if they are not right-angled. You just need to ensure you are using the correct base and height!

The area, A, of a triangle is one-half the product of the triangle's base and height.

Explore how to calculate the area of a triangle using the formula A = 1/2 × base × height. This problem demonstrates both the general and specific applications of the formula, suitable for students in Grades 6-8.

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