Question

Can someone Please show me how to do this Thank you
What is the surface area of the prism?



A.138 yd2


B.192 yd2


C.264 yd2


D.272 yd2

Answer 1

To find the surface area, you need to find the area of all the sides and then add them up.

Answer 2

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The two triangles outlined in blue are congruent. Find the area of 1, and multiply that area by 2 or just add the area's together.

Answer 3

the book shows to uses these formulas and when you plug everything in it does not match the answers

Answer 4

what are the formulas they give you?

Answer 5

SA=2B+PH
B=1/2BH

Answer 6

and then it shows to get the perimeter

Answer 7

Hmm. I think those formulas make it a little confusing. Do you mind if I show you a simpler way to remember how to find Surface area?

Answer 8

please do
thank you

Answer 9

Ok. When I need to find the surface area, you just need to remember that you have to find the area of the surface. Like, you can see different shapes that make up the prism given. There's the two triangles and a few rectangles. What you have to do to find the surface area. Is find the area of all those little shapes. Then once you found the area of those shapes, add them together. Let's start with the rectangles. I'll outline the one we'll do first in blue.

http://prntscr.com/6zikur

The area formula of a rectangle is \[Length \times Width\]Those are the two numbers given. All you need to do to find the area is multiply them together. What do you get when you do that? \[10\times9\]

Answer 10

so you take 10x9=90 like that

Answer 11

Yep. Now you know one area. Let's find another area.
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I outlined the rectangle in blue again.

Answer 12

then you find the 2 areas of the triangle which is 24 then add everything together 90+24+24=138

Answer 13

You have the right idea to add. But the area of the triangle isn't correct. We have to find the area's of the other rectangles first.

Answer 14

oh ok

Answer 15

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We have to find those areas first. Do you want to do the one outlined in red first or the one in blue?

Answer 16

blue

Answer 17

ok.
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We need to multiply \[6\times9\]

Answer 18

54

Answer 19

would the red be 8x9

Answer 20

Right, what do you get when you multiply that?

Answer 21

72

Answer 22

so you add everything together 264
24+24+90+54+72

Answer 23

Yep. We have 90, 54, and 72. We can find the triangles now.

Triangles have a different area formula. It's \[ \frac{ l \times h}{ 2 }\]

Answer 24

Yep, 264 is the right answer. :)

Answer 25

so you break every shape down and then add them all together,your way is way easier then what there trying to show Thank you so much

Answer 26

:) You're welcome.

Answer 27

I can try. You'll do the same thing.

http://prntscr.com/6zisde

There's a rectangle hiding beside the red and yellow colors.

Answer 28

There's a million ways you could try to break that shape down, but that's how I seen it.

Answer 29

ok so if we do blue it woud be 4x15

Answer 30

Yep.

Answer 31

red would be 9x15

Answer 32

Right.

Answer 33

yellow would be 9x4

Answer 34

Yep. Keep going. :D

Answer 35

green would be 6x6

Answer 36

Yes.

Answer 37

peach would be the same 6x6

Answer 38

You have the first 6 right. But look again.
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Answer 39

or would it be 4x6

Answer 40

Yep. 6x4

Answer 41

now do we add it all together?

Answer 42

There's also the one we can't see and the bottom of the shape. Since the shape is 3d, some of the sides have backs.

Answer 43

ok we would just add the peach # twice same with the Green #?

Answer 44

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There's shapes under the red. Behind the blue and beside the red and yellow.

Add green twice, but peach doesn't need to be added 2 times. Red does. Green and red are added twice.

Answer 45

http://prntscr.com/6ziwuo
There's that shape. and we need the bottom, too.

http://prntscr.com/6zix3f

Answer 46

After that, you'll be done.

Answer 47

ok let me add them all together and see what I get

Answer 48

Right.

Answer 49

Hmm my answers doesn't equal the answers to pick from let me break it down and maybe you can see my mistake

Answer 50

So:
Blue-15x4
red-15x9
red-15x9
green-6x6
green-6x6
peach-6x4
yellow-6x4
side-9x4
bottom-15x4

Answer 51

oops. I think I forgot another shape :/
http://prntscr.com/6ziyuh

Answer 52

60+135+135+36+36+24+24+36+60=546

Answer 53

would that one be 6x4

Answer 54

yep. 6x4. I think that's where we went wrong.

Answer 55

hmm the answers still dont match haha sorry this is taking so long

Answer 56

what are your options?

Answer 57

900
582
399
291

Answer 58

huh. @confluxepic do you know where we went wrong?

Answer 59

cause I get 570 adding it all together

Answer 60

I get the same answer. I don't think we missed any shapes, but I'm not sure.

Answer 61

It may take me a while since I will be reading every post in this question. @k_lynn

Answer 62

ok. do you mind @kenzie707 ?

Answer 63

no not at all

Answer 64

okie doke.

Answer 65

For the big rectangle at the side:
\(\large\ 8\times 9=72\)

For the two triangles:
The are of a triangle is \(\large\frac{1}{2}6\times 8=24\)
Double that to get the area of both the triangles which is 48.
\(\large(\frac{1}{2}6\times 8)(2)=48\)

For the bottom rectangle:
\(\large\ 9\times 6=54\)

For the slanted rectangle at the top:
\(\large\ 10\times 9=90\)

Now add them all up.
\(\large\ 72+48+54+90=264\)

Answer 66

opps not that one this one

Answer 67

Oh wait. I did the wrong question.

Answer 68

Do you have to find the volume or the surface area?

Answer 69

surface area

Answer 70

Ok.

Answer 71

Did you forget to add the surface are of the hidden part?

Answer 72

http://prntscr.com/6zj6b3
That part?

Answer 73

http://prntscr.com/6zj6gc

Answer 74

I remember seeing that and start to type that we needed to remember that one, but I forget if I did mention it. SO no, I don't think we added that.

Answer 75

Then that's probably the mistake.

Answer 76

That would have been where we messed up @kenzie707 we still have to add that part.

Answer 77

Thanks @confluxepic

Answer 78

Thanks Confluxepic

Answer 79

No problem. :)

Answer 80

\(\color{blue}{\text{Originally Posted by}}\) @k_lynn
So:
Blue-15x4
red-15x9
red-15x9
green-6x6
green-6x6
peach-6x4
yellow-6x4
side-9x4
bottom-15x4
\(\color{blue}{\text{End of Quote}}\)
other side:

Answer 81

What are we going to multiply @kenzie707 to get the invisi-side

Answer 82

6x4?

Answer 83

yes.

Answer 84

what do you get because my answer still doesnt match

Answer 85

My answer doesn't match either.

Answer 86

weird I will ask the teacher

Answer 87

okie doke.

Answer 88

Thank you for all your help

Answer 89

Sure, no problem. Glad to help you.