To find the area of the triangle formed by the points A(2, 4), B(9, 4), and C(3, 2) using their coordinates, we can use the formula for the area of a triangle given by its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Substituting the coordinates of the points:
- \(A (x_1, y_1) = (2, 4)\)
- \(B (x_2, y_2) = (9, 4)\)
- \(C (x_3, y_3) = (3, 2)\)
We plug these values into the formula:
\[ \text{Area} = \frac{1}{2} \left| 2(4 - 2) + 9(2 - 4) + 3(4 - 4) \right| \]
Calculating each term:
\[ = \frac{1}{2} \left| 2 \cdot 2 + 9 \cdot (-2) + 3 \cdot 0 \right| \] \[ = \frac{1}{2} \left| 4 - 18 + 0 \right| \] \[ = \frac{1}{2} \left| -14 \right| \] \[ = \frac{1}{2} \cdot 14 = 7 \]
Thus, the area of the triangle is \(7\) square units.
The answer is \(7\).