Question

A rectangular prism with a square base has a lateral area of 192 square yards and a surface area of 264 square yards. What is the length of a base edge?

Answer 1

A rectangular prism is like a cardboard shoe box. It has two equal bases, one on the top and the other on the bottom. It also has 4 lateral faces to close the figure. The surface area of the prism is the area of all its faces: the 4 side faces and the 2 bases. On the other hand, lateral surface area only accounts for the 4 lateral faces. Therefore, we can conclude that the total surface area is equal to the lateral surface area plus the areas of the two bases.

TSA = LSA + 2s²

Since the base is said to be the square, its area is equal to s² where s is the base edge. Because there are 2 bases, that's why it's 2s².

264 = 192 + 2s²
s² = (264-192)/2
s = √36
s = 6 yards