Question

Describe a method you can use to find the area of the following shape. Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure. (8 points)
The shape looks like this in points (1,0) to (3,-5) to (1,-8) to (-5,-8) to (-3,-6) to (-5,-3) then back to the starting point (1,0)

Answer 1

The area of figure ABCDEF can be computed as the sum of the areas of trapezoid ACDF and triangle ABC, less the area of trangle DEF.
  trapezoid ACDF area = (1/2)(AC +DF)·(CD) = (1/2)(8+5)(6) = 39
  triangle ABC area = (1/2)(AC)(2) = 8
  triangle DEF area = (1/2)(DF)(2) = 5

Area of ABCDEF = (ACDF area) + (ABC area) - (DEF area) = 39 +8 -5 = 42

The actual area of ABCDEF is 42 square units.