That's an easy parallelogram, parallel to the x axis. Let's label the points
A(-4,-1),B(-2,4),C(4,4),D(2,-1)
AD and BC are the sides parallel to the x axis. We'll call those the base, it has length 4 - -2 = 6.
The height is the change in y between the bases, so 4 - -1 = 5.
The area is base times height, 6 × 5 = 30
Answer: 30
The shoelace formula gives us the area of a polygon from 2D coordinates without worrying about the shape:
(-4,-1),(-2,4),(4,4),(2,-1)
(-2,4),(4,4),(2,-1),(-4,-1)
[tex]A = \frac 1 2 | -4(4) - (-1)(-2) + (-2)(4) - 4(4) + 4(-1) - 4(2) + 2(-1) - (-1)(-4) |[/tex]
[tex]A = \frac 1 2 |-60| = 30 \quad \checkmark[/tex]
