To calculate the area of a triangle given its vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, we use the formula:

$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

The coordinates of the triangle's vertices are:

• $A(2, 4)$
• $B(9, 4)$
• $C(3, 2)$

Now, applying these values into the formula:

$\text{Area} = \frac{1}{2} \left| 2(4 - 2) + 9(2 - 4) + 3(4 - 4) \right|$

Simplifying:

$\text{Area} = \frac{1}{2} \left| 2(2) + 9(-2) + 3(0) \right|$ $\text{Area} = \frac{1}{2} \left| 4 - 18 + 0 \right|$ $\text{Area} = \frac{1}{2} \left| -14 \right|$ $\text{Area} = \frac{1}{2} \times 14 = 7$

Thus, the area of the triangle is 7 square units.

Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:

1. How would the formula change if one of the vertices had negative coordinates?
2. Can you calculate the perimeter of this triangle based on the given coordinates?
3. How do you find the centroid of a triangle using its vertex coordinates?
4. What is the significance of using absolute value in the area formula?
5. How would the area formula differ if you were working with a 3D triangle?

Tip: When working with coordinate geometry, always ensure to keep track of signs and perform careful arithmetic operations, especially with negatives.