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

Refer to the figure below. There are other ways to split up the five sided polygon. I added in point F(2,-2) to help with labeling of the smaller pieces.

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Part B

Answers:

AB = 4 units

AE = 5 units

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Explanation:

Count out the number of spaces between points A and B to find that there are 4 spaces. Therefore, segment AB is 4 units long. You could also subtract the x coordinates and apply absolute value.

For segment AE, it's the same idea. Though it's slightly different in that you subtract y coordinates this time.

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Part C

Answer: 31 square units

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Explanation:

Rectangle ABFE is 4 by 5 as mentioned in part B earlier. The area of this rectangle is 4*5 = 20 square units.

Triangle CED has base of CE = 7 and height 1 unit. Its area is base*height/2 = 7*1/2 = 3.5 square units.

Triangle CFB has base FC = 3 and height FB = 5. Its area is base*height/2 = 3*5/2 = 7.5 square units.

Add up the smaller areas to get the grand total area.

rectangle+triangle1+triangle2 = 20+3.5+7.5 = 31