To calculate the area of triangle ABC with vertices A(1,4), B(4,1), and C(-3,1), we can use the formula for the area of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Plugging in the coordinates of the points A(1,4), B(4,1), and C(-3,1):
- \( x_1 = 1, y_1 = 4 \)
- \( x_2 = 4, y_2 = 1 \)
- \( x_3 = -3, y_3 = 1 \)
Now substituting these values into the area formula:
\[ \text{Area} = \frac{1}{2} \left| 1(1 - 1) + 4(1 - 4) + (-3)(4 - 1) \right| \]
Calculating each term:
\[ = \frac{1}{2} \left| 1(0) + 4(-3) + (-3)(3) \right| = \frac{1}{2} \left| 0 - 12 - 9 \right| = \frac{1}{2} \left| -21 \right| = \frac{1}{2} \times 21 = 10.5 \]
Therefore, the area of triangle ABC is 10.5 square units.