Question

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? Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE.
Part C: What is the area of Figure ABCDE? Show your work.

Answer 1

Given : Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2).

To Find : Plot the points  

Decompose Figure ABCDE into rectangles and triangles.

lengths of Sides AB and AE.

area of Figure ABCDE

Solution:

Plot ( x , y)

if x is +ve go right from origin if negative then go left

for y go upward if +ve , in case of -ve go downward

Points plotted and labelled

A(−3, 3), B(2, 3),

length of AB =  5

A(−3, 3) E(−3, −2).

Length of AE = 5

One rectangle and two triangle

area of rectangle  = 5 * 5  = 25 sq units

area of right angle triangle = (1/2) * 5 * 3  = 7.5 sq units

area of another triangle = (1/2) * 8 * 1 = 4 Sq units

Area of figure  = 25 + 7.5 + 4  = 36.5 sq units

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Answer 2

Answer:

Part A: I made 5 triangles and I made 3 rectangles.

Part B: The length between Point A and B is 4 units and the length between point A and E is 5 units.

Part C: The area of figure ABCDE is 34.5 because I made a Rectangle that is 20 units I made a triangle which is 2 units and I made another triangle which is 5 units and I made 1 more triangle which is 7.5 units.

Step-by-step explanation:

I did the test and the instructor said I was right.