Question

What is the area of this figure

Answer 1

 First, you must observe the figure and realize that you have a parallelogram and a rectangle.
 Therefore, the total area will be the sum of the area of the parallelogram plus the area of the rectangle.
 Palelogram area:
  A1 = b * h
  We have then
  b = root ((- 4 - (- 10)) ^ 2+ (2-2) ^ 2) = 6
  h = root ((- 7 - (- 7)) ^ 2+ (3-2) ^ 2) = 1
  A1 = (6) * (1) = 6 units ^ 2
  Rectangle area
  A2 = L * W
  We have then:
   L = root ((1 - (- 2)) ^ 2 + (- 3 - (- 4)) ^ 2) = 3.16227766
   W = root ((- 4 - (- 2)) ^ 2+ (2 - (- 4)) ^ 2) = 6.32455532
   A2 = (3.16227766) * (6.32455532)
   A2 = 20 units ^ 2
   The total area is the sum of both ares:
   A = A1 + A2
   A = 6 + 20
   A = 26 units ^ 2
   Answer:
   the area of this figure
   A = 26 units ^ 2