Question

This figure is made up of a rectangle and parallelogram.

Answer 1

Given the coordinates of two points, P1 and P2, the distance formula between these two points is deduced.
 d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
 To find the area of the figure we must first find the area of the rectangle and add the area of the parallelogram.
 rectangle area
 A = (L) * (w)
 L = root ((- 6-2) ^ 2 + (- 1-1) ^ 2) = 8.25
 w = root ((- 6 - (- 5)) ^ 2 + (- 1 - (- 5)) ^ 2) = 4.12
 A = (8.25) * (4.12) = 33.99
 Parallelogram area
 A = (b) * (h)
 b = root ((3-3) ^ 2 + (3 - (- 3)) ^ 2) = 6
 h = root ((3-2) ^ 2 + (3-3) ^ 2) = 1
 A = (6) * (1) = 6
 The total area is then
 Atotal = 33.99 + 6 = 39.99 units ^ 2
 Answer
 the area of this figure is 39.99 units ^ 2