The area of the base of a prism is 21 cm2. The perimeter of the base is 20 cm. The height of the prism is 8 cm.
What is the surface area of the prism?

- anonymous

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- anonymous

@dan815
@♪Chibiterasu

- anonymous

@satellite73 @SolomonZelman @Miracrown @micahm @UsukiDoll @Astrophysics

- anonymous

can some one help me

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## More answers

- micahm

openstudy.com/updates/54e4ad6ce4b0aba126e81022
copy and paste this in a new window

- MrNood

you do not know the shape of the base but you do knw the perimeter
when you make the base int a prism you end up with a number of rectagular sides
the height of EACH of these rectangles is 8 and the summ of ALL their widths is 20
so - what isa the area of all the side faces?

- anonymous

i already saw that it doesn't help

- anonymous

@micahm

- micahm

https://www.google.com/search?q=The+area+of+the+base+of+a+prism+is+21+cm2.+The+perimeter+of+the+base+is+20+cm.+The+height+of+the+prism+is+8+cm.+What+is+the+surface+area+of+the+prism%3F&rlz=1C1GGGE___US571US573&oq=The+area+of+the+base+of+a+prism+is+21+cm2.+The+perimeter+of+the+base+is+20+cm.+The+height+of+the+prism+is+8+cm.+What+is+the+surface+area+of+the+prism%3F&aqs=chrome..69i57&sourceid=chrome&es_sm=122&ie=UTF-8#q=The+area+of+the+base+of+a+prism+is+21+cm+2.+The+perimeter+of+the+base+is+20+cm.+The+height+of+the+prism+is+8+cm.+What+is+the+surface+area+of+the+prism?

- anonymous

i know that but don't know how to get the answer

- MrNood

|dw:1449753823180:dw|
you have a number of rectangular vertical faces the sum of their bases is 20, and ALL have a height of 8
so what is their area?

- MrNood

|dw:1449753945397:dw|

- anonymous

so

- anonymous

how do i get the answer

- welshfella

you can find the dimensions of the base by solving the system of 2 equations
2w + 2l = 20
lw = 21
wher l and w are the length and width
i am assuming that the base is rectangular

- MrNood

so
have a little think
do a little work
discuss your working here....

- anonymous

k

- anonymous

can u show how to do get the answer

- MrNood

@welshfella
you cannot make that asumption
and oyu do not need to
all the sides bottom edges ADD to 20
all the sides height is 8
so you can work out the total area just from that info

- anonymous

u can't

- anonymous

16

- anonymous

@♪Chibiterasu

- anonymous

can u show me how to get the answer

- MrNood

yes you can
you do not know haow many edges there are
but if they were of lenght a,b,c,d .... etc
then the area of 1 side would be 8a, then 8b + 8 c etc
8a+8b + 8c +...... = 8(a+b+c+......)
but you know that the sum of a+b+c+..... = 20
so there is the answer to the area of the sides

- anonymous

@dan815 @Anaise @AloneS @Daniellelovee @Deadly_Roses @dakid88 @Diana.xL @gibbs @HELLOMYNAMEISKAM @HS_CA @hoots89 @helpppppppppp @jameskang1015 @jebonna @jakyfraze @Joehoffy @Johan14th

- dakid88

Allright. A prism is a 3 faced structure made of equilateral triangles

- welshfella

@MrNood yes you are right

- MrNood

I assume by tagging all those people you are expecting one of them to give oyu the answer
I have given you ALL except the last step to working outth esides
The prism also has 2 identical ends - and oyu know the area of 1 end is 21

- dakid88

let one side be x.
the perimiter of the base, 3x = 20

- dakid88

The surface area of a prism = 2 × area of base + perimeter of base × H

- MrNood

@dakid88
that is not correct
a Prism is ANY polygon base shape - NOT just a triangle
You are thinking of a pyramid
My answer above works for ALL prisms

- anonymous

u are not showing me how to get to the last step

- dakid88

yes the answer is 2

- gibbs

go to tiger-algebra.com

- MrNood

a = the answer is not 2
b I am not giving you the last step because you are studying maths and the best way to learn is to DO
just do what I gave you above
work out the area of the sides, and then add the area of TWO ends

- gibbs

it shows you how to do it and it gives the answer

- MrNood

OR
do a little work and feel a little self satisfaction and pride

- anonymous

k

- anonymous

nonon

- anonymous

i meant lead me to the last step

- MrNood

I have led you all the way:
here it is again - you just need to make 1 step from here...
you do not know how many edges there are
but if they were of lenght a,b,c,d .... etc
then the area of 1 side would be 8a, then 8b + 8 c etc
8a+8b + 8c +...... = 8(a+b+c+......)
but you know that the sum of (a+b+c+....) = 20
so there is the answer to the area of the sides

- anonymous

it can only be 2.5 or 2.4

- anonymous

3 is the answer

- MrNood

|dw:1449755063343:dw|

- anonymous

i get it the closest answer is 3

- MrNood

you have not posted any options

- anonymous

there is no option

- MrNood

so - if the area of just 1 end is 21 HOW can the total be 3?

- anonymous

7

- welshfella

The total area of the sides of the prism = perimeter of the base * height (8)

- anonymous

=20

- MrNood

I have told him that several times above - he is not even beginning to think about this
I'm out

- anonymous

i don't get it

- anonymous

it is 2.5

- anonymous

@Demonx341

- anonymous

@Englishguy

- anonymous

@Demonx341

- anonymous

@gibbs http://tiger-algebra.com/ does not help

- gibbs

fine check here http://www.mathpapa.com/algebra-calculator.html

- MrNood

@super123
do you want to understand this?

- anonymous

no

- anonymous

@welshfella @Willie579 @Wendy.Ivette11714 @wwhitlock @Ephemera @Emiwock @Englishguy @ethan726 @explicitvogue @They_Call_Me_Narii @the_ocean_girl @TypnoEchosis @Theanitrix @twister02 @YoungStudier @YumYum247 @you_me @yb1996 @Yuna123 @UsukiDoll @uybuyvf @IloveHW @izzyrawrz @INeedYourHelpBad @I_Ask_Alot @IHelpYouLearn @Owlcoffee @okdutchman7 @otaylor19 @oreolo @phi @poopsiedoodle @puppylover52 @PenguinRulez @popcornfun @Astrophysics @AloneS @Anaise @AbdullahM @ash_heather1 @secret66 @sweetburger @seb.cal @DLS @Daniellelovee @Destinycholie @Deadly_Roses @dakid88 @DariusX @FortyTheRapper @flamingpiano @fashionguru12 @green_1 @gibbs @G@girlmeetsworld @gracea @HELP!!!! @HELLOMYNAMEISKAM @HS_CA @hoots89 @helpppppppppp @jameskang1015 @jebonna @jakyfraze @jordanpipes @jacobyoungbleed @♪Chibiterasu

- welshfella

imagine that the prism has no end bases and its made of thin cardboard
if we cut vertically down the length and spread it out it would look like the following
|dw:1449756104192:dw|

- anonymous

160

- welshfella

- rectangular piece of cardboard are 8 * 20 = 160 cm2 in area
agreed?

- anonymous

k

- welshfella

yes so you just add on the areas of the 2 bases ( 2 times 21) and you have your answer

- anonymous

320

- anonymous

6720

- welshfella

No
160 + (2 times 21) = ?
do the multiplication first

- anonymous

202

- anonymous

is it

- anonymous

@welshfella

- welshfella

yes 202 cm2 is correct

- anonymous

that is the answer

- welshfella

that is the answer

- anonymous

a medal 4 u and i will make a new ?

- anonymous

k

- welshfella

ok

- welshfella

The assumption that the base is a rectangle can be made and the method of solving the system of equations will give the correct solution though it is a more involved method than the above.

- MrNood

@welshfella
The fact is the answer is the same for ANY base shape from 3 to n sides
you cannot 'assume' that the answer for 4 sides is true for ALL - but it IS true that the answer for ALL (as I gave) IS true for your assumption of rectangle.
There is nothing in the question to say rectangle - so you are likely to make a mistake if you assume things that are not given

- welshfella

I was merely saying that the answer will be the same if you assume that the base is a rectangle.

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