Final answer:
To find the area of a polygon with given vertices, you can use the Shoelace formula. The area of the polygon with the given vertices A(-5,-2), B(4,-2), C(4,-7), and D(-5,-7) is -56 units squared.
Step-by-step explanation:
To find the area of a polygon with given vertices, you can use the Shoelace formula. The formula for the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is:
A = 0.5 * [(x1*y2 + x2*y3 + ... + xn*y1) - (x2*y1 + x3*y2 + ... + x1*yn)]
In this case, the vertices of the polygon are A(-5,-2), B(4,-2), C(4,-7), and D(-5,-7). Substituting the x and y coordinates into the formula, we get:
A = 0.5 * [(-5*-2 + 4*-7 + 4*-2 + -5*-7) - (-2*4 + -7*4 + -2*-5 + -7*-5)]
Simplifying the expression, we find that the area A is equal to -56 units squared.