Aright square pyramid has a slant height of 13 inches and a lateral area of 260 square inches. what is the volume of the pyramid to the nearest cubic inch?

260/4 = 65 square inches is area of a side 
area of a side = base*height/2 = base *13/2

65 = b*13/2

130=b*13

b = 10 so the side length equal 10 inches 

area of base = 10*10 = 100 

volume of a pyramid = area of base time height /3 

(the height of pyramid)^2 = 13^2 - 5^2

h^2 = 169 -25 = 144 

h = 12 

V = area of base time height /3 = 100*12/3 = 400 cubic inches 

hope this will help you