Final answer:
To find the area of the trapezoid formed by points P(1, 2), Q(3, 1), R(8, 1), and S(-4, -5), you can use the distance formula to find the lengths of the bases and the height, and then apply the formula for the area of a trapezoid.
Step-by-step explanation:
The trapezoid formed by points P(1, 2), Q(3, 1), R(8, 1), and S(-4, -5) can be analyzed using the properties of trapezoids. To find the length of the bases, we can use the distance formula. The length of the base PQ is sqrt(2), the length of the base RS is 12, and the height of the trapezoid is 7. Using the formula for the area of a trapezoid, which is (1/2) * (base1 + base2) * height, we can calculate the area of the trapezoid as 47 square units.