Question

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.

Answer 1

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

Answer 2

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

Answer 3

what is AB mean?

Answer 4

prolly height of pyrimaid

Answer 5

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

Answer 6

B is on the bottom

Answer 7

pentagonal 5 sides

Answer 8

looks good

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

yes

Answer 14

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

Answer 15

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

Answer 16

this is what I got so far;

I can calculate the missing parts the hard way... but thats just how I role lol

Answer 17

ha oh boy

Answer 18

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

Answer 19

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

Answer 20

:) I get about 85 there ... if I did it right but *5

gotta chk it again make sure I aint messed it up

Answer 21

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

Answer 22

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

Answer 23

I get abt 440.5 for the bottom area that way

Answer 24

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

Answer 25

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

h = 8 tan(54)

Answer 26

16/2 = 8

8 * 8tan(54) = area of red tri

5* area red tri = area base

Answer 27

= 215.6

Answer 28

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

Answer 29

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

Answer 30

is 10 slant and 8 side

Answer 31

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

Answer 32

that 215.6 is off

Answer 33

I thought the apothem was 5.5

Answer 34

aint that the slant?

Answer 35

http://www.wolframalpha.com/input/?i=area+pentagon+side+%3D16

I keep coming to 440.442 as area of base

Answer 36

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

Answer 37

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

pentagonal pyramid

Answer 38

5.5 16 10 is what I used

Answer 39

Sa = 620 ....

220
440.5
------ so we are close
660.5

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

thats my lingo... lol

Answer 44

I was trying to describe whatever you were asking

Answer 45

:) does my interpretation for this look good then?

Answer 46

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

Answer 47

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

Answer 48

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

Answer 49

where alll the edges meet and creat the pentagonal base

Answer 50

yes

Answer 51

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

Answer 52

AB is a side of one of them triangles

Answer 53

the tiny dancer is what I have pictured

Answer 54

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

Answer 55

then:

Sa = 5(face area) + 5(redbase area)

Sa = 5(5.5*16/2) + 5(8*8tan(54)/2)

Sa = 660.442

Answer 56

16*8tan(54)/2 lol

Answer 57

oh wow...

Answer 58

we got a way to verify this?

Answer 59

yea that calulator if I know the right numbers

Answer 60

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

Answer 61

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..

Answer 62

85.8253

slnat height is 10? and sides are 5

Answer 63

do you know how to do a screenshot?

Answer 64

no

Answer 65

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

press it

Answer 66

k

Answer 67

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

Answer 68

yes

Answer 69

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

Answer 70

is that what you wanted?

Answer 71

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

Answer 72

the problem is is in my book

Answer 73

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

Answer 74

ok hang on

Answer 75

ok

Answer 76

is that what you wanted LOL

Answer 77

yes :)

Answer 78

kk

Answer 79

the apothem of the pentagon is 5.5 ; thats the length from the center of the base out to the base edge... much better

Answer 80

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

Answer 81

this is the correct picture I needed lol

Answer 82

I still get 200

Answer 83

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 ....

Answer 84

what did we determine the slant length is

Answer 85

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

Answer 86

9.16

Answer 87

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

Answer 88

9.17

Answer 89

Sa = 293.303

Answer 90

how guaranteed.... I get 366.6

Answer 91

is side 10 or 8?