Question

On a coordinate plane, trapezoid A B C D has points (negative 5, negative 2), (negative 1, 2), (0, negative 1), (negative 2, negative 3).
Trapezoid ABCD is graphed in a coordinate plane.

What is the area of the trapezoid?

10 square units
12 square units
20 square units
24 square units

Answer 1

12 square units

Using the shoelace formula for vertices in order A(-5,-2), B(-1,2), C(0,-1), D(-2,-3):

Sum x_i*y_{i+1} = (-5)(2)+(-1)(-1)+0(-3)+(-2)(-2) = -10+1+0+4 = -5
Sum y_i*x_{i+1} = (-2)(-1)+2(0)+(-1)(-2)+(-3)(-5) = 2+0+2+15 = 19

Area = (1/2)|-5 - 19| = (1/2)(24) = 12.