To find the area of the triangle with vertices at points \( A(0, 3) \), \( B(10, 6) \), and \( C(6, 3) \), we can use the formula for the area of a triangle given by the coordinates of its vertices:
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Plugging in the coordinates:
- \( A(x_1, y_1) = (0, 3) \)
- \( B(x_2, y_2) = (10, 6) \)
- \( C(x_3, y_3) = (6, 3) \)
We can substitute these into the formula:
\[ \text{Area} = \frac{1}{2} \left| 0(6 - 3) + 10(3 - 3) + 6(3 - 6) \right| \] \[ = \frac{1}{2} \left| 0 + 10 \cdot 0 + 6(-3) \right| \] \[ = \frac{1}{2} \left| 0 - 18 \right| \] \[ = \frac{1}{2} \cdot 18 = 9 \]
Thus, the area of the triangle is \( \boxed{9} \) square units.
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