Question 965309
You want the height of the pyramid so you could use volume as {{{(1/3)h*s^2}}}, where s is side length of the base and h is height of pyramid.  The given slant height will help you find the pyramid height.


Let slant height be L, and h be pyramid height, and s be base edge length.
The slant height is the hypotenuse of a triangle with legs s/5 and L.


{{{h=sqrt((s/5)^2+L^2)}}}


You have for this,
{{{h=sqrt((10/2)^2+13^2)}}}
{{{h=sqrt(25+169)}}}
{{{h=sqrt(194)}}}


Your volume is {{{(1/3)sqrt(194)10^2}}} which you can simplify.