The lateral area of the right prism is L= Ph, where P is the perimeter of the base of the solid and h is the height of the solid.
112.5 square inches
Practice makes perfect
We are asked to find the lateral area of the given solid. First, let's analyze the given prism. We will assume that the prism is right. Otherwise, we have too little data to solve the exercise.
Note that the lateral area of a right prism is given by the formula L= Ph, where P is the perimeter of the base of the solid and h is the height of the solid. This tells us that h= 5 inches. Since the base is an equilateral pentagon, its perimeter is P=5* 4.5= 22.5 inches. Now, let's find L.
Therefore, the lateral area of the solid is 112.5 square inches.
Extra
Shape of the Base
In the base there is an equilateral pentagon. Does that mean there is a regular polygon in the base? Notice that even if every edge of a pentagon is the same, that is not enough for it to be considered regular. This is the same for quadrangles, too — look at a square and a rhombus.
Just one of the two equilateral pentagons presented is regular.
