If the lateral surface area of a square pyramid is 84ft^2 and the base edge is 6, what is the slant height?

The slanting height of the pyramid will be calculated as follows;

lateral area is given by:

Area=[area of the base]+4[area of triangular sides]

area of the base will be:

Area=length*width

=6*6=36 ft^2

area of triangular sides will be:

[84-36]

=48 ft^2

area of one triangle will be:

48/4=12 ft^2

but

area of triangle is given by:

area=1/2bh

hence the height will be:

12=1/2*6*h

12=3h

h=12/3

h=4 ft

the answer is 4 ft