Question

Find the volume for the regular pyramid.

Answer 1

@surjithayer

Answer 2

@Ahmad1

Answer 3

the volume= 1/3*the area of the base* height
right or it's the slant height?

Answer 4

yes that is right

Answer 5

okay , now we have to evaluate the area of this polygon, do u remember a direct rule I should try to find it by deviding it into three triangles?

Answer 6

or I should**

Answer 7

Since you just need to find the area of the base couldn't you just evaluate that and add it into the formula?

Answer 8

lol yes I can , but I forgot what's the rule the area of the polygon

Answer 9

oh! im sorry! haha the rule for area of a pentagon is A=\[\frac{ 1 }{ 2 }ap\]

Answer 10

is this what you needed?

Answer 11

\[\frac{ 1 }{ 2 }apothem timesperimeter\]

Answer 12

that's "apothem times perimeter"

Answer 13

yes thank you, but I still don't understand what does apothem mean lol
anyways you certainly do so we have the area of the pentagon

Answer 14

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.

Answer 15

Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word "apothem" can also refer to the length of that line segment. Regular polygons are the only polygons that have apothems. Because of this, all the apothems in a polygon will be congruent and have the same length.

Answer 16

I think I found it!

Answer 17

i got \[3\sqrt{8}\]

Answer 18

okay thank you so much , looks like im getting more benifet than you
I tried many time to draw but I couldn't I accurately make one

Answer 19

sure?

Answer 20

haha! its alright! but thank you for your help!:)

Answer 21

oh wait that's not the right answer.... haha!

Answer 22

so I think now a clever guy like you can figure the height himself. right :P

Answer 23

oops! we did not sub in the equation of the volume yet @mollsy

Answer 24

also you did not find the height

Answer 25

isn't the height also considered the apothem?

Answer 26

or is it considered the slant height?

Answer 27

I don't think so , I cant draw any figure to proof!! it's kinda hard with these tools
can you imagine the right triangle formed by the slant height, apothom,and height ?

Answer 28

this where you can get the height ;)

Answer 29

could i figure out the altitude by using the Pythagorean theorem?

Answer 30

if i subbed in \[h ^{2}\]

Answer 31

lol, that's what Im trying to say

Answer 32

so that it is a\[a ^{2}+b ^{2}=c ^{2}\]

Answer 33

\[h^2=6^2-(3\sqrt{8})^2\]

Answer 34

oh... haha

Answer 35

but this looks impossible to me :\

Answer 36

yeah i'll try solving it myself and if i don't get i'll just come back!

Answer 37

it's the apothom which is wrong my friend it must be smaller , you try and I'll try to find it and tell

Answer 38

okay

Answer 39

i got \[144\sqrt{3}\] but somehow i don't think its right. haha

Answer 40

OMG! it's very impossible

Answer 41

can you tell me please what's th measure of the angles?

Answer 42

it's given by some rule as I remember

Answer 43

or maybe it is 48\[\sqrt{3}\]

Answer 44

i mean 48*square root 3

Answer 45

i'll try that

Answer 46

I wish I can come next to you and see how you get these results :P

Answer 47

haha i'll just skip this problem and move to the next

Answer 48

no no I actually got the apothhom in terms of the angle
it's \[4\sin(\theta/2)\] but still need to know theta!
look like u don't study very well my friend :P just go back to the book and look for the rule of the angle of the regular polygon I'm sure you well get it