Expert: Richard J. Raridon - 12/19/2004

Question
Quadrilateral JAME has vertices J(2,-2),A(8,-1),M(9,3), and E(3,2). Prove that quadrilateral Jame is a parallelogram and find its area.
Forget the proving part as I figured that out, but can you please show me how to get the area?Thanks.

Answer
There's more than one way to get the area but a simple method is as follows:
Draw the rectangle (2,-2),(2,3),(9,3),(9,-2)
The area of that rectangle is 7*5 = 35 units.
At the upper left and lower right of the rectangle, draw a unit square.  That should leave you with four triangles.  
The area of the left and right triangles is each 2 and the upper and lower triangles is each 3.  
Subtract those and the unit squares from the rectangle and
you get 35 -1 -1 -2 -2 -3 -3 = 23 units for the parallelogram.