Question 1193447
Find the volume of a square pyramid if each base edge and each lateral edge equals {{{36cm}}}.

You have right-angled triangle, formed by the altitude, the edge of the pyramid and half of the diagonal.

half of the diagonal of square base is:

{{{d/2=sqtr(36^2+36^2)/2=sqrt(2*36^2)/2=36sqrt(2)/2=18sqrt(2)}}}

{{{h^2=36^2-(18sqrt(2))^2}}}

{{{h^2=1296-648}}}

{{{h^2=648}}}

{{{h=sqrt(648)}}}

{{{h=18sqrt(2)cm}}}


volume is:


{{{V= (1/3)* (Base_ Area)(Height)}}}


{{{V= (1/3)* (36cm*36cm)(18sqrt(2)cm)}}}


{{{V= 12cm*36cm*18sqrt(2)cm}}}


{{{V=10997cm^3 }}}