SOLUTION: A church steeple in the shape of a regular square pyramid needs to be reshingled. Before the shingles of the steeple are replaced, an exhaust fan is to be installed in the steeple.

Consider one lateral triangular face.

Lateral edge, the slant height and half of the base edge make a right-angled triangle with 
the hypotenuse of 15 ft and one leg of 18/2 = 9 ft.


Refering to standard (3,4,5) right-angled triangle, we conclude the the other leg is 12 ft.


This other leg is the slant height, so the slant height is 12 ft long.  

It is the ANSWER to question (a).



Next, the altitude of the pyramid, the slant height and the apothem of the square base make
another right angled triangle with the hypotenuse of 12 ft (the slant height)
and one leg of 18/2 = 9 ft (the apothem of the square).


It gives   =  =  ft  for the altitude of the pyramid.

It is the answer to question (b).



The area of the square base is the base edge squared   = 324 sq.ft.
It is the answer to question (c).



The volume of the pyramid is 1/3 of the base area times altitude

    V =  =   cubic feet.

It is the answer to question (d).