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.

- anonymous

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- anonymous

Surface area = 200 cm^2
can anyone see if this is right?

- amistre64

apothem is the face height and not the pyramid height right?

- amistre64

what is AB mean?

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## More answers

- amistre64

prolly height of pyrimaid

- 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

B is on the bottom

- anonymous

pentagonal 5 sides

- amistre64

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- anonymous

looks good

- amistre64

8*5.5*5 is side areas, do we include the bottom as well?

- anonymous

l^2 = (5.5)^2 + (4)^2
l = sqrt 5.5^2 + 4^2
sqrt
yea... I think I did

- anonymous

sqrt 30.25 + 16
sqrt 46.25
p = 6.8
1/2(40)(6.8) + 8^2
= 200

- 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

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- anonymous

yes

- amistre64

8 * 5 * 5.5 = 220 for sides areas .... but to include the base we'd have to do some more calculations

- anonymous

ok well its just asking for the surface area.... LA + B

- 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

ha oh boy

- 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

oh wow... so um... tell me you get 200 LOL

- 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

hah!! i had 72 but used 74 lol .....

- anonymous

ok I'll check again too... good eye

- amistre64

I get abt 440.5 for the bottom area that way

- anonymous

i wonder if there is a calculator to find the area... let me investigate LOL

- amistre64

i think I see an easier way; tan(54) = h/8
h = 8 tan(54)

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- amistre64

16/2 = 8
8 * 8tan(54) = area of red tri
5* area red tri = area base

- amistre64

= 215.6

- amistre64

220
215.6
-------
435.6 abt for the surface areas

- anonymous

hey whats the side length, and what is the slant length

- anonymous

is 10 slant and 8 side

- amistre64

the side length of the pyramid is 10; and the slant is 5.5

- amistre64

that 215.6 is off

- anonymous

I thought the apothem was 5.5

- amistre64

aint that the slant?

- amistre64

http://www.wolframalpha.com/input/?i=area+pentagon+side+%3D16
I keep coming to 440.442 as area of base

- anonymous

the calculator is asking for
apothem length
side length
slant length
enter height

- anonymous

http://easycalculation.com/area/pyramid.php
pentagonal pyramid

- amistre64

5.5 16 10 is what I used

- amistre64

Sa = 620 ....
220
440.5
------ so we are close
660.5

- amistre64

edge base length is what I cant be to sure about; how do you describe that?

- anonymous

ha your awesome.... hey it says round to the nearest tenth unit...

- anonymous

the edge where the number is in my book LOL on AB?

- anonymous

thats my lingo... lol

- anonymous

I was trying to describe whatever you were asking

- amistre64

:) does my interpretation for this look good then?

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- amistre64

if I got the 8 in the right place... then im good to go

- anonymous

the 8s are at the bottom of base of the pyramid

- amistre64

yes; the red is just a reflection into the base under the pyramid

- anonymous

where alll the edges meet and creat the pentagonal base

- amistre64

yes

- anonymous

A is the top of the pyramid.... and B is at the bottom with the 8s

- anonymous

AB is a side of one of them triangles

- amistre64

the tiny dancer is what I have pictured

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- anonymous

well there it is!!! yep looks just like it LOL

- amistre64

then:
Sa = 5(face area) + 5(redbase area)
Sa = 5(5.5*16/2) + 5(8*8tan(54)/2)
Sa = 660.442

- amistre64

16*8tan(54)/2 lol

- anonymous

oh wow...

- amistre64

we got a way to verify this?

- anonymous

yea that calulator if I know the right numbers

- anonymous

I dunno... I'm going with what you did!

- 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

85.8253
slnat height is 10? and sides are 5

- amistre64

do you know how to do a screenshot?

- anonymous

no

- amistre64

do you see the "PrtScrn" key that you never use up there with the "pause", and "scroll lock" keys?
press it

- anonymous

k

- amistre64

now open up your 'paint' program and hit your 'ctrl + v' keys to paste it. and let me know if it worked

- anonymous

yes

- amistre64

save it to your desktop as a jpeg and attach it to this post

- anonymous

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- anonymous

is that what you wanted?

- amistre64

yep; now do that to the screen that has the problem on it :)

- anonymous

the problem is is in my book

- amistre64

can you take a picture of it? and put it on the computer? maybe a scanner?

- anonymous

ok hang on

- anonymous

ok

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- anonymous

is that what you wanted LOL

- amistre64

yes :)

- anonymous

kk

- 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

just an FYI regular pyramid formula is LA + B
Yes , i thought I told you that :)

- amistre64

this is the correct picture I needed lol

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- anonymous

I still get 200

- 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

what did we determine the slant length is

- 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

9.16

- amistre64

http://www.wolframalpha.com/input/?i=5%284*sqrt%2810^2-4^2%29%29%2B5%284*5.5%29

- anonymous

9.17

- amistre64

Sa = 293.303

- anonymous

how guaranteed.... I get 366.6

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- amistre64

is side 10 or 8?

- amistre64

height should be abt 7.331

- anonymous

side is the top of pyramid AB 10 no??? whats 8? base I dunno

- anonymous

who ever invented math is wasting valuable life time for me!!! :(

- amistre64

... the base of this thing is abt 110.1111

- anonymous

thats the perimeter of the base... 5(8) = 40 I thought

- amistre64

183.303 is the lateral area
110.111
--------
293.414

- amistre64

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- anonymous

Ok I give up on this one... I am taking your word!

- amistre64

and this for the base lol

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- anonymous

you have some neat sites

- anonymous

when I think I understand .... I DONT!!!

- amistre64

:) thnx take a break, and get aome air

- amistre64

I gotta drive up to the veranda and setup for my laptop; librarys closing...

- anonymous

ok ... I need to review... take my notes... and on to the next.. LOL
Thank you

- anonymous

I'll be here!!

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