If a rectangular prism has a surface area of 198 square feet, a height of 6 feet and a lateral surface area of 144 square feet what is the base area of the prism? What is the volume of the prism?

Answer 1

length --- x
width ---- y
height ---- 6

volume = 6xy

The most common definition of lateral surface is the sum of all the surfaces of the object except the base.

So the sum of all six sides of our box is 198
the sum of the 5 sides , that is, excluding the base , is 144
so the area of the base = 196-144 = 52

but the area of the base is xy
so xy = 52
volume = 6xy = 6(52) = 312 ft^3