anonymous
  • anonymous
Find the surface area of the regular pentagonal pyramid. The apothem of the pentagon is 5.5cm and AB =10 cm. The edge base length at the bottom of the figure is 8cm. Round answers to the nearest tenth of a unit.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Surface area = 200 cm^2 can anyone see if this is right?
amistre64
  • amistre64
apothem is the face height and not the pyramid height right?
amistre64
  • amistre64
what is AB mean?

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amistre64
  • amistre64
prolly height of pyrimaid
anonymous
  • anonymous
apothem is a line segment from the center of the polygon perpendicular to one of its sides.... AB is ... A is the tip of the pyramid... to the base.. an edge of a side
anonymous
  • anonymous
B is on the bottom
anonymous
  • anonymous
pentagonal 5 sides
amistre64
  • amistre64
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anonymous
  • anonymous
looks good
amistre64
  • amistre64
8*5.5*5 is side areas, do we include the bottom as well?
anonymous
  • anonymous
l^2 = (5.5)^2 + (4)^2 l = sqrt 5.5^2 + 4^2 sqrt yea... I think I did
anonymous
  • anonymous
sqrt 30.25 + 16 sqrt 46.25 p = 6.8 1/2(40)(6.8) + 8^2 = 200
amistre64
  • amistre64
sqrt((4^2) + (5.5^2)) = 6.80073525 doesnt = 10 sqrt((8^2) + (5.5^2)) = 9.7.... is close to 10 If the edge AB that runs slong the side is 10, that means the base is 16
amistre64
  • amistre64
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anonymous
  • anonymous
yes
amistre64
  • amistre64
8 * 5 * 5.5 = 220 for sides areas .... but to include the base we'd have to do some more calculations
anonymous
  • anonymous
ok well its just asking for the surface area.... LA + B
amistre64
  • amistre64
this is what I got so far; I can calculate the missing parts the hard way... but thats just how I role lol
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anonymous
  • anonymous
ha oh boy
amistre64
  • amistre64
16^2 = 2s^2 -2s^2 cos(74) 16^2 = s^2(2-2cos(74)) 16^2 -------- = s^2 2-2cos(74) Area in red = (s^2 sin(74))/2
anonymous
  • anonymous
oh wow... so um... tell me you get 200 LOL
amistre64
  • amistre64
:) I get about 85 there ... if I did it right but *5 gotta chk it again make sure I aint messed it up
amistre64
  • amistre64
hah!! i had 72 but used 74 lol .....
anonymous
  • anonymous
ok I'll check again too... good eye
amistre64
  • amistre64
I get abt 440.5 for the bottom area that way
anonymous
  • anonymous
i wonder if there is a calculator to find the area... let me investigate LOL
amistre64
  • amistre64
i think I see an easier way; tan(54) = h/8 h = 8 tan(54)
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amistre64
  • amistre64
16/2 = 8 8 * 8tan(54) = area of red tri 5* area red tri = area base
amistre64
  • amistre64
= 215.6
amistre64
  • amistre64
220 215.6 ------- 435.6 abt for the surface areas
anonymous
  • anonymous
hey whats the side length, and what is the slant length
anonymous
  • anonymous
is 10 slant and 8 side
amistre64
  • amistre64
the side length of the pyramid is 10; and the slant is 5.5
amistre64
  • amistre64
that 215.6 is off
anonymous
  • anonymous
I thought the apothem was 5.5
amistre64
  • amistre64
aint that the slant?
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=area+pentagon+side+%3D16 I keep coming to 440.442 as area of base
anonymous
  • anonymous
the calculator is asking for apothem length side length slant length enter height
anonymous
  • anonymous
http://easycalculation.com/area/pyramid.php pentagonal pyramid
amistre64
  • amistre64
5.5 16 10 is what I used
amistre64
  • amistre64
Sa = 620 .... 220 440.5 ------ so we are close 660.5
amistre64
  • amistre64
edge base length is what I cant be to sure about; how do you describe that?
anonymous
  • anonymous
ha your awesome.... hey it says round to the nearest tenth unit...
anonymous
  • anonymous
the edge where the number is in my book LOL on AB?
anonymous
  • anonymous
thats my lingo... lol
anonymous
  • anonymous
I was trying to describe whatever you were asking
amistre64
  • amistre64
:) does my interpretation for this look good then?
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amistre64
  • amistre64
if I got the 8 in the right place... then im good to go
anonymous
  • anonymous
the 8s are at the bottom of base of the pyramid
amistre64
  • amistre64
yes; the red is just a reflection into the base under the pyramid
anonymous
  • anonymous
where alll the edges meet and creat the pentagonal base
amistre64
  • amistre64
yes
anonymous
  • anonymous
A is the top of the pyramid.... and B is at the bottom with the 8s
anonymous
  • anonymous
AB is a side of one of them triangles
amistre64
  • amistre64
the tiny dancer is what I have pictured
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anonymous
  • anonymous
well there it is!!! yep looks just like it LOL
amistre64
  • amistre64
then: Sa = 5(face area) + 5(redbase area) Sa = 5(5.5*16/2) + 5(8*8tan(54)/2) Sa = 660.442
amistre64
  • amistre64
16*8tan(54)/2 lol
anonymous
  • anonymous
oh wow...
amistre64
  • amistre64
we got a way to verify this?
anonymous
  • anonymous
yea that calulator if I know the right numbers
anonymous
  • anonymous
I dunno... I'm going with what you did!
amistre64
  • amistre64
ive been trying to define apothem, slant heaight, and all that stuff; but nothing is consistant. apothem of a pyramid most likely means the height of a face; slant height also means distance up the face; so I cant seem to determine what any of it really means..
anonymous
  • anonymous
85.8253 slnat height is 10? and sides are 5
amistre64
  • amistre64
do you know how to do a screenshot?
anonymous
  • anonymous
no
amistre64
  • amistre64
do you see the "PrtScrn" key that you never use up there with the "pause", and "scroll lock" keys? press it
anonymous
  • anonymous
k
amistre64
  • amistre64
now open up your 'paint' program and hit your 'ctrl + v' keys to paste it. and let me know if it worked
anonymous
  • anonymous
yes
amistre64
  • amistre64
save it to your desktop as a jpeg and attach it to this post
anonymous
  • anonymous
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anonymous
  • anonymous
is that what you wanted?
amistre64
  • amistre64
yep; now do that to the screen that has the problem on it :)
anonymous
  • anonymous
the problem is is in my book
amistre64
  • amistre64
can you take a picture of it? and put it on the computer? maybe a scanner?
anonymous
  • anonymous
ok hang on
anonymous
  • anonymous
ok
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anonymous
  • anonymous
is that what you wanted LOL
amistre64
  • amistre64
yes :)
anonymous
  • anonymous
kk
amistre64
  • amistre64
the apothem of the pentagon is 5.5 ; thats the length from the center of the base out to the base edge... much better
anonymous
  • anonymous
just an FYI regular pyramid formula is LA + B Yes , i thought I told you that :)
amistre64
  • amistre64
this is the correct picture I needed lol
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anonymous
  • anonymous
I still get 200
amistre64
  • amistre64
Sa = 5(8*sqrt(10^2+4^2)/2) + 5(8*5.5/2) Sa = 5(4*sqrt(116)) + 5(4*5.5) Sa = 20sqrt(116) + 20(5.5) Sa = 325.406592 ....
anonymous
  • anonymous
what did we determine the slant length is
amistre64
  • amistre64
the slant length is the missing leg of the right tri formed by half the base and a hyp of 10 sh^2 + 4^2 = 10^2 sh = sqrt(100 - 16) .. doh!! I added
anonymous
  • anonymous
9.16
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=5%284*sqrt%2810^2-4^2%29%29%2B5%284*5.5%29
anonymous
  • anonymous
9.17
amistre64
  • amistre64
Sa = 293.303
anonymous
  • anonymous
how guaranteed.... I get 366.6
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amistre64
  • amistre64
is side 10 or 8?
amistre64
  • amistre64
height should be abt 7.331
anonymous
  • anonymous
side is the top of pyramid AB 10 no??? whats 8? base I dunno
anonymous
  • anonymous
who ever invented math is wasting valuable life time for me!!! :(
amistre64
  • amistre64
... the base of this thing is abt 110.1111
anonymous
  • anonymous
thats the perimeter of the base... 5(8) = 40 I thought
amistre64
  • amistre64
183.303 is the lateral area 110.111 -------- 293.414
amistre64
  • amistre64
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anonymous
  • anonymous
Ok I give up on this one... I am taking your word!
amistre64
  • amistre64
and this for the base lol
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anonymous
  • anonymous
you have some neat sites
anonymous
  • anonymous
when I think I understand .... I DONT!!!
amistre64
  • amistre64
:) thnx take a break, and get aome air
amistre64
  • amistre64
I gotta drive up to the veranda and setup for my laptop; librarys closing...
anonymous
  • anonymous
ok ... I need to review... take my notes... and on to the next.. LOL Thank you
anonymous
  • anonymous
I'll be here!!

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