This is important Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles.

Part A: How many triangles and rectangles did you make? (1 point)

Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points)

Part C: What is the area of Figure ABCDE? Show your work. (5 points)

d

Step-by-step explanation:

There's a right angle that they want you to make a rectangle out of.  I'm ignoring that and using each of the five sides to make a triangle with the origin.

A.  Five triangles, zero rectangles.

B.

AB=4, the difference of the x coordinates since the y coordinates are the same

AE = 5, the difference in the y coordinates since the x coordinates are the same

C.  We'll use the Shoelace Formula, adding up all those triangles I made.  A triangle with vertices (0,0), (a,b), (c,d) has signed area A = (1/2)(ad-bc).  We go around counterclockwise so they all have positive areas, starting with AE, then ED, DC, CB, BA.

Area = (1/2) (  (-2)(-2) - 3(-2)  +  (-2)(-4) - (-2)(0)  +  0(-2) - (-4)(5)  + 5(3) - (-2)(2) + 2(3) - (3)(-2))

Area = 69/2