Figure ABCDE has vertices A(−2, 3), B(2, 3), C(5, −2), D(0, −4), 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)

- anonymous

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- anonymous

@DarkMoonZ

- anonymous

@Michele_Laino

- anonymous

How would i do this? im confused on how to solve this.

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## More answers

- Michele_Laino

I'm doing the drawing of your points...

- anonymous

Ok should i get graph paper?

- Michele_Laino

I think that it is better

- anonymous

i can't find it nvm

- Michele_Laino

|dw:1438892480757:dw|

- Michele_Laino

next step:
|dw:1438892648200:dw|

- Michele_Laino

next step:
|dw:1438892711601:dw|

- Michele_Laino

I got two rectangles and two triangles

- anonymous

Yes it looks really good

- anonymous

to find the length of in units of Sides AB and AE how would i do that i keep forgetting what to do

- Michele_Laino

you have to compute the difference between the x-coordinates or y.coordinates. For example:
\[\Large \begin{gathered}
AB = 2 - \left( { - 2} \right) = ... \hfill \\
AE = 3 - \left( { - 2} \right) = ... \hfill \\
\end{gathered} \]

- Michele_Laino

the distance has to be always a positive number

- anonymous

4

- Michele_Laino

AB=4, ok!
and AE=...?

- anonymous

i got 5

- Michele_Laino

that's right!

- anonymous

Whoop whoop! (:

- Michele_Laino

the area of our polygon is given by the sum of the areas of the two rectangles and two triangles

- anonymous

So i do what i just did for all of them now for c?

- Michele_Laino

|dw:1438893214246:dw|

- Michele_Laino

area of rectangle ABPQ=
PQ*AP=4* 3=...?
being PQ= AB= 4,a nd AP = 3-0=3

- anonymous

12

- Michele_Laino

ok!
next:
area of rectangle PQER:
ER*EP= 4*2=...
being ER=AB=4
EP=0-(-2)=2

- anonymous

8

- Michele_Laino

correct!

- Michele_Laino

nexT:
area of triangle ECD=
EC*HD=...?
being EC=5-(-2)=7
HD=-2-(-4)=2
|dw:1438893545943:dw|

- Michele_Laino

next*

- Michele_Laino

oops...
area of triangle ECD=
(EC*HD)/2=...?

- anonymous

11

- anonymous

and

- Michele_Laino

we have:
area of triangle ECD=
EC*HD=(7*2)/2=...?

- anonymous

7

- Michele_Laino

correct!

- Michele_Laino

next step:
are of triangle BRC=
BR*RC/2=...?
being:
BR=3-(-2)=5
RC=5-2=3

- anonymous

7.5? is it 5x3x1/2?

- Michele_Laino

that's right!

- anonymous

yay!

- Michele_Laino

so area of our polygon is:
12+8+7+7.5=...?

- anonymous

34.5!!

- Michele_Laino

yes! correct!

- anonymous

Yes im so happy when you help me i understand it better.

- Michele_Laino

thanks! :)

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