Hi, I've been working on a problem which I thought would be quite easy - but the answer I got was incorrect. Can someone please help me?

In a certain regular square pyramid, all of the edges have length 12. Find the volume of the pyramid.

Thank you so much!!!

Caffeine Jul 3, 2020

#1**0 **

the formula for the volume of a pyramid is length*width*height/3. We know the length and the width but we don't know the height. Since we know this is a regular pyramid, and we know all edges have the length of twelve, we can draw a triangle with the information we know

height^2 + (1/2*length)^2 = k^2(where k is the length from any corner to the tip of the pyramid.) know we plug in the information we know.

height^2 + 36 = 144

height^2 =108

height = 6 root 3.

so then we plug in those values in to the formula for a pyramid and get 12*12*6 root 3 /3

= 4*12*6root3

=48*6(sqrt108) = 1728*sqrt(3)

Guest Jul 3, 2020

#2**0 **

1) Diagonal of a square **d = sqrt( 12 ^{2} + 12^{2 }) = 16.97056275 d/2 = 8.485281374**

2) Height of a pyramid **h = sqrt( 12 ^{2} - 8.485281374^{2} ) = 8.485281374 ()**

3) Volume of the pyramid **V = lwh/3 = (12*12*8.485281374) /3 = 407.293506 u ^{3 }**

Guest Jul 3, 2020

#3**0 **

Hello, Guest!

" height = 6 root 3 " this is slant height

You need the altitude (height) of the pyramid to calculate the volume.

I'll use your slant height to find the height of the pyramid.

**h = sqrt[( 6*√3) ^{2} - 6^{2} ] = sqrt( 108 - 36 ) = 8.485281374 **

Guest Jul 3, 2020