To determine the area of a quadrilateral given its vertices, we can divide the quadrilateral into two triangles, calculate the area of each triangle, and then sum the areas.

Given the vertices are $(-14, -2)$, $(10, 10)$, $(-10, -10)$, and $(4, -24)$, let's consider two triangles:

1. Triangle 1 with vertices $(-14, -2)$, $(10, 10)$, and ((-10, -10