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!