Question

What is the area of this figure ?

Answer 1

 Remember that what you must do for this case is to calculate the area of the parallelogram and add it to the area of the rectangle.
  Palelogram area:
  Knowing the base and the height, the area of the parallelogram is calculated by its formula: 
  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