Question

Find the perimeter of this trapezoid.

A(2, 1), B(6, 5), C(3, 5), D(1, 3)

Answer 1

Do you know the distance formula?

Answer 2

Use the distance formula for all the vertices and add them up.

Answer 3

no

Answer 4

I will demonstrate one time and then you can practice.

Answer 5

I mean, I don't know how to use it for this..

Answer 6

@Mertsj thanks

Answer 7

\(\Large \color{MidnightBlue}{\Rightarrow D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\)

Answer 8

what about perimeter?

Answer 9

is that going to be the same as diameter for this?

Answer 10

You add up the distances of all the lines.

Answer 11

Choose two of the given points and plug into the distance formula.

Answer 12

Start with A and B

Answer 13

Sketch it, then see all the vertices. Apply the distance formula for all lines and then add the distances to get the perimeter.

Answer 14

That will give you the length of side AB.

Answer 15

@Mertsj is a perfect teacher, I'll let him continue

Answer 16

I think he left!

Answer 17

alright.. sketching..

Answer 18

\[AB=\sqrt{(6-2)^2+(5-1)^2}=\sqrt{16+16}=4\sqrt{2}\]

Answer 19

@rokotherodent did you understand?

Answer 20

Now you try BC

Answer 21

A little bit..

Answer 22

And enough of this talk about diameter. Diameter is a characteristic of a circle. We're dealing with a trapezoid here.

Answer 23

@ParthKohli I'm a little confused..

Answer 24

Thanks @Mertsj because I wanted perimieter

Answer 25

I may help you understand. Where are you confused btw?

Answer 26

well, I've drawn the trapezoid.. but then

Answer 27

So find the length of BC. It's an easy one because 5-5=0

Answer 28

Think about the distance between two points by using the distance formula.

Answer 29

what do I need? Do I need AB, BC, CD, and thats all?

Answer 30

When you add the lengths of all sides, you get the perimeter.

Answer 31

Remember that perimeter is the distance around. So find the length of each side and add them together.

Answer 32

Trapezoid = four sides

Answer 33

so BC = sqrt 9 (3)?

Answer 34

\[BC=\sqrt{(6-3)^2+(5-5)^2}=\sqrt{3^2+0^2}=\sqrt{9}=3\]

Answer 35

(6,5)(3,5)

\(\Large \color{MidnightBlue}{\Rightarrow \sqrt{(6 - 3)^2 + 0^2} }\)
\(\Large \color{MidnightBlue}{\Rightarrow \sqrt{3^2} }\)
\(\Large \color{MidnightBlue}{\Rightarrow 3 }\)
Am I correct?

Answer 36

Yes, you both are!

Answer 37

This is what I have..

Answer 38

Can you do it now?

Answer 39

Now lastly, I have one more question: the blank has 6 sqrt _

Answer 40

do I just put 3 in that blank then?

Answer 41

You add the lengths of all sides. Remember.

Answer 42

So far we have this start:
Perimeter = AB + BC + CD + AD = 4sqrt2+3 + CD + AD

Answer 43

So if we could just find CD and AD we would have it!!

Answer 44

ok

Answer 45

Yep!

Answer 46

CD is sqrt 4

Answer 47

AD is sqrt 2

Answer 48

Hmm no

Answer 49

\[CD=\sqrt{(5-3)^2+(3-1)^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\]

Answer 50

So now we have Perimeter = AB + BC+CD+AD=4sqrt2+3+2sqrt2+AD
Try AD again.

Answer 51

Follow the distance formula.

Answer 52

ok
2 - 1 = 1
1 - 3 = neg. 2

Answer 53

@Mertsj I'm 99 now ^_^

Answer 54

Squaare them now.

Answer 55

okay, 2 squared is 4

Answer 56

And square them....then find the square root

Answer 57

What is 1 squared?

Answer 58

What is \(\sqrt{1 + 4}\)?

Answer 59

1 + 4 = 5

Answer 60

Yes. Now add all the lengths.

Answer 61

Good. So AD=?

Answer 62

sqrt 5?

Answer 63

Yes

Answer 64

AD = sqrt 5

Answer 65

now, adding them together..

Answer 66

Yes. Now add all four sides and remember that only similar radicals can be added.

Answer 67

Now add the side lengths:
4sqrt2+3+2sqrt2+sqrt5

Answer 68

ok

Answer 69

so that will be 6 sqrt 2 + 3 sqrt 5?

Answer 70

@ParthKohli I see that you are 99 now. How did that happen so quickly?

Answer 71

Well but, I don't think you should change 3 + sqrt5 to 3 TIMES sqrt5, do you?

Answer 72

Result of hard work from the day I joined the site aka 22 April lol

Answer 73

ok I agree @Mertsj

Answer 74

I think that the final answer will be: 6 sqrt 2 + sqrt 5 + 3

Answer 75

So why don't we just leave it 6sqrt2+3+sqrt5 since there are no other like terms that can be added.

Answer 76

Well, I thought that we could in fact leave it at that.

Answer 77

And you are correct and now we know how far it is around that trapezoid.!!!

Answer 78

Yes, you could. Unlike terms.

Answer 79

Finally done...ahh

Answer 80

Thanks to both! I appreciate your help!

Answer 81

you're welcome :D

Answer 82

yw and we hope you have learned a lot.

Answer 83

Can you do the rest?

Answer 84

I have! I have an identical problem that I'll work myself! :D @ParthKohli

Answer 85

Sure....! If you have any confusion then contact me or Mertsj.

Answer 86

Excellent. And then if you want someone to check it you have ParthKohli's number.

Answer 87

Alrighty! thanks!