1: Use lateral area sum to find the perimeter of the bottom surface, and then find the side length of the bottom surface.

2. Use the side length of the bottom to find the bottom area.

3. After calculating the bottom area, calculate the volume by formula V=SH.

Answer: Because the side area is 48√3 and the height is 4. Then we can get the bottom circumference C=V/H= 12√3.

Because it is a regular hexagonal prism, the bottom surface is an equilateral regular hexagon. Then its base length is 12√3/6=2√3. Knowing the side length of the bottom surface, we can find out the area of the bottom surface.

The area formula of a regular hexagon is: s =1.5 √ 3a 2 (the literal expression is the square of 3 times the root number and 3 times the side length).

Then its bottom area is 18√3. The volume can be obtained by knowing the bottom area, so V=SH= 18√3*4=72√3.

Analysis: The key to finding the volume of a regular prism is to require the bottom area to be high.