SOLUTION: A right pyramid on a base of 4cm square has a slant edge of 6cm. Calculate the volume of the pyramid

I believe that the pyramid is REGULAR, which means that its base is a square.


If so, then the side of this square is  = 2 cm,
 
and the diagonal of the square is  cm.



Draw the height (the altitude) of the pyramid from the upper vertex to the base of the pyramid.


You will get a right-angled triangle with one leg on the base as the half
of the diagonal of the square, so the length of this leg is   cm long.


The hypotenuse of this right-angled triangle is 6 cm (it is the slant edge).


Hence, by Pythagoras, the altitude is  h =  =  =   cm.


Thus the volume of the pyramide is 

     =  =  = 7.7746 cm^3  (approximately).    ANSWER