I did try to do this but seriously don't know if what i'm doing is right. Do I have to do pythagorean theorem?

RainbowPanda Dec 3, 2018

#1**+2 **

The perimeter is all solved using the distance formula, RP

The formula for the distance between two points is given by

√ [ (subtract the x coordinates of the two points)^2 + (subtract the y coordinates)^2 ]

So....for instance....the distance between A and B is

√ [ ( -2 - 2)^2 + ( -1 -1)^2 ] = √ [ (-4)^2 + (-2)^2] = √ [16 + 4] = √20 = 2√5

Now..using this example..compute the distances between

A and D

D and C

C and B

Add these four distances....this will be the perimeter

Do this part first....then....I will show you how to calculate the area

Let me know if you run into trouble......

CPhill Dec 3, 2018

#2**+1 **

I got:

2sqrt(5) for A and D

sqrt(3i) for D and C

C and B is sqrt(9) sqrt(5)

RainbowPanda
Dec 3, 2018

#3**+2 **

AD is correct !!!

And you got BC correct.... we can simplify it as 3√5

Let's look at DC.....

√ [ ( -4 - (-1) )^2 + ( -5 - (-5) )^2 ] = √ [ ( -3)^2 + ( 0 )^2] = √9 = 3

So.... the perimeter is

AB + AD + DC + BC =

2√5 + 2√5 + 3 + 3√5 =

7√5 + 3 units ≈ 18.65 units

You did pretty well....!!!!

The area is a little tricky, RP.....I'll get back to it in just a bit.....I have a few more questions to get to....just hold on...!!!

CPhill Dec 3, 2018

#4**+2 **

Area....

We have a quadrilateral with two parallel sides AD and BC...so....this is a trapezoid

The area is

(1/2) height of trapezoid * ( sum of the base lengths)

The bases are DC and AB.....we know these

The height is the tricky part....it is found as:

[ The y coordinate of B - The y coordinate of C ] = [ 1 - (-5) ] = [ 1 + 5] = 6 units

So.....the area is

(1/2) (6) ( 3 + 2√5 ) ≈ 22.42 units^2

And that's it....!!!

CPhill Dec 3, 2018