Question

create a rectangle around the parallelogram. the dimensions of this rectangle are
find the area of the four right triangles surrounding the parallelogram. the total area of the triangles is square units.
subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. the area of parallelogram abcd is square units.

Explanation:

Step1: Find rectangle dimensions

The rectangle will span from the minimum to maximum x and y values of the parallelogram's vertices.
Minimum x: $-3$, Maximum x: $8$ → Width = $8 - (-3) = 11$
Minimum y: $-11$, Maximum y: $9$ → Height = $9 - (-11) = 20$
Dimensions: $11$ units (width) × $20$ units (height)
Area of rectangle: $11 \times 20 = 220$

Step2: Calculate area of 4 triangles

Triangle 1 (top-left, near A(-3,-1)):

Base = $|-3 - (-2)| = 1$, Height = $|-1 - (-11)| = 10$
Area = $\frac{1}{2} \times 1 \times 10 = 5$

Triangle 2 (top-right, near B(7,9)):

Base = $8 - 7 = 1$, Height = $9 - (-1) = 10$
Area = $\frac{1}{2} \times 1 \times 10 = 5$

Triangle 3 (bottom-left, near D(-2,-11)):

Base = $|-2 - (-3)| = 1$, Height = $9 - (-1) = 10$
Area = $\frac{1}{2} \times 10 \times 1 = 5$

Triangle 4 (bottom-right, near C(8,-1)):

Base = $8 - 7 = 1$, Height = $9 - (-11) = 20$? No, correct: Base = $8 - 7 = 1$, Height = $9 - (-1) = 10$ → No, correct vertices: Triangle near C: vertices (8,-1), (7,9), (8,9): Base=$1$, Height=$10$, Area=$5$. Wait, correct matching:
Actual four triangles:

1. A(-3,-1), (-3,9), B(7,9): Base=$10$, Height=$10$ → Area=$\frac{1}{2} \times 10 \times 10 = 50$
2. B(7,9), (8,9), C(8,-1): Base=$1$, Height=$10$ → Area=$\frac{1}{2} \times 1 \times 10 = 5$
3. C(8,-1), (8,-11), D(-2,-11): Base=$10$, Height=$10$ → Area=$\frac{1}{2} \times 10 \times 10 = 50$
4. D(-2,-11), (-3,-11), A(-3,-1): Base=$1$, Height=$10$ → Area=$\frac{1}{2} \times 1 \times 10 = 5$

Total area of triangles: $50 + 5 + 50 + 5 = 110$

Step3: Find parallelogram area

Subtract total triangle area from rectangle area:
$220 - 110 = 110$

Answer:

Dimensions of the rectangle: $\boldsymbol{11 \times 20}$ square units
Total area of the triangles: $\boldsymbol{110}$ square units
Area of parallelogram ABCD: $\boldsymbol{110}$ square units