Question

Parallelogram
On a coordinate plane, parallelogram A B C D is shown. Point A is at (negative 3, negative 1), point B is at (7, 9), point C is at (8, negative 1), and point D is at (negative 2, negative 11).

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.

Answer 1

The bounding rectangle has x from -3 to 8 and y from -11 to 9, so its dimensions are 11 by 20 and its area is 11·20 = 220.

The four right triangles around the parallelogram have areas:
- top-left: (1/2)(10)(10) = 50
- top-right: (1/2)(1)(10) = 5
- bottom-right: (1/2)(10)(10) = 50
- bottom-left: (1/2)(1)(10) = 5

Total area of the triangles = 50 + 5 + 50 + 5 = 110 square units.

Area of parallelogram = rectangle area − triangle areas = 220 − 110 = 110 square units.