Question

using the box method to calculate the area of a parallelogram
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
a(-3, -1)
b(7, 9)
c(8, -1)
d(-2, -11)

Explanation:

Step1: Find rectangle dimensions

The length of the rectangle in the x - direction is from $x=-3$ to $x = 8$, so the length $l=8-(-3)=11$. The height of the rectangle in the y - direction is from $y=-11$ to $y = 9$, so the height $h=9-(-11)=20$. The dimensions of the rectangle are $11\times20$.

Step2: Calculate area of each right - triangle

There are 4 right - triangles.
For the two pairs of congruent right - triangles:
One pair of right - triangles: base $b_1 = 5$, height $h_1=10$. Area of one such triangle $A_1=\frac{1}{2}\times5\times10 = 25$.
The other pair of right - triangles: base $b_2 = 6$, height $h_2 = 10$. Area of one such triangle $A_2=\frac{1}{2}\times6\times10=30$.
The total area of the 4 right - triangles $A_{triangles}=2\times25 + 2\times30=50 + 60=110$.

Step3: Calculate area of parallelogram

The area of the rectangle $A_{rectangle}=11\times20 = 220$.
The area of the parallelogram $A = A_{rectangle}-A_{triangles}=220 - 110=110$.

Answer:

The dimensions of the rectangle are $11\times20$, the total area of the triangles is $110$ square units, and the area of parallelogram $ABCD$ is $110$ square units.