To calculate the area of the triangle formed by the points \( A(-5, -4) \), \( B(3, -3) \), and \( C(3, 2) \), we can use the formula for the area of a triangle given by its vertices:
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the vertices.
Assigning the points:
- \( A(x_1, y_1) = (-5, -4) \)
- \( B(x_2, y_2) = (3, -3) \)
- \( C(x_3, y_3) = (3, 2) \)
Substituting the points into the area formula:
\[ \text{Area} = \frac{1}{2} \left| -5(-3 - 2) + 3(2 - (-4)) + 3((-4) - (-3)) \right| \]
Calculating each term step by step:
- \( -5(-3 - 2) = -5(-5) = 25 \)
- \( 3(2 - (-4)) = 3(2 + 4) = 3 \times 6 = 18 \)
- \( 3((-4) - (-3)) = 3(-4 + 3) = 3(-1) = -3 \)
Putting it all together:
\[ \text{Area} = \frac{1}{2} \left| 25 + 18 - 3 \right| \] \[ = \frac{1}{2} \left| 40 \right| \] \[ = \frac{1}{2} \times 40 = 20 \]
Thus, the area of Leonardo's triangle is \( \boxed{20} \) square units.