16
First, determine the lengths of each side by using the Pythagorean theorem.
Distance between (-3,-1) and (1,3)
sqrt((-3 - 1)^2 + (-1 -3)^2)
= sqrt(-4^2 + -4^2)
= sqrt(16 + 16)
= sqrt(32)
= 4sqrt(2)
Do the same thing to determine the distances between the other vertexes
Distance (1,3) to (3,1) = 2sqrt(2)
Distance (3,1) to (-1,-3) = 4sqrt(2)
Distance (-1,-3) to (-3,-1) = 2sqrt(2)
We now know that the rectangle has a length of 4sqrt(2) and a height of 2sqrt(2). Since the area is simply the product of those two values, we get:
4sqrt(2) * 2sqrt(2) = 4 * 2 * sqrt(2)*sqrt(2) = 4 * 2 * 2 = 16.
