Question

Find the volume for the regular pyramid.

Answer 1

the volume of regular pyramid is 1/3 * base area * height
can u find the height ?

Answer 2

i tried and then everything was wrong..

Answer 3

ok, so lets take simpler thing first,
area of base.
since its a regular pyramid, the base is an equilateral triangle.
Area of equilateral triangle ?

Answer 4

4 root 3?

Answer 5

its 3/4 * side^2 = (3/4) *4*4 = ?

Answer 6

root 3 over 4...

Answer 7

1/3 X area-of-base X perpendicular height = Volume of pyramid

Answer 8

@angelicapad

Answer 9

put x=4

Answer 10

formula for an equilateral triangle is s^2 * root3/4

Answer 11

ok sorry, so root 3 /4 *4*4 = 4 root 3, thats correct, i m sorry.

Answer 12

yaa

Answer 13

so whats the problem

Answer 14

now , we just need to find height.

Answer 15

so 4 root 3 represents what exactly?

Answer 16

the problem is just that every number i come up with, comes up wrong

Answer 17

the slant height(s) is also 4 here, so we can use the formula to get the height(h)
\(s^2 = h^2 + a^2/12\)
4 root 3 is just the area of base
we need to multiply by height and 1/3 to get the volume.

Answer 18

what is a?

Answer 19

a is the length of base , also = 4 here

Answer 20

a little confused on the formula

Answer 21

i got it from this source :
http://mathworld.wolfram.com/TriangularPyramid.html

Answer 22

wait i found one more easier formula here :
http://www.mathsisfun.com/geometry/triangular-pyramid.html

Answer 23

base area + 0.5 * perimeter * side length

Answer 24

perimeter?

Answer 25

nevermind, that was for surface area.

Answer 26

oh

Answer 27

i have a different problem if you want to help me with that instead?

Answer 28

i wish the height was given here, it makes the solution very simple...
and yes, whats the other problem ?

Answer 29

lateral area

Answer 30

that is a hexagonal pyramid

Answer 31

yeah

Answer 32

ok, height is given then its easy
u can find slant height using, pythagoras theorem

Answer 33

\(\sqrt{8^2+6^2}\)

Answer 34

10

Answer 35

ok, we need to find apothem of pyramid...u know how to ?

Answer 36

i suck at that -.-

Answer 37

ok, here's the formula :
slant ht.^2 = apothem^2 +(base side/2)^2<----pythagoras theorem
so
10^2=Ap^2+3^2

Answer 38

Ap = \(\sqrt{91}\)

Answer 39

ahhh, i got that right!

Answer 40

now lateral surface area = Ap * perimeter of base /2

Answer 41

perimeter of base = 6* sides = 6*6 = 36

Answer 42

lateral area = 36/2 * \(\sqrt{91}\) = 18 \(\sqrt{91}\) =

Answer 43

171.7

Answer 44

thats all i had to put, it said it was right :) 18 root 91
thank you! again haha

Answer 45

ok, welcome...
trying 1st problem ?
volume

Answer 46

no its fine :) after i got the last one right it said i was done because i got over 90%

Answer 47

congrats !