What is a Prism ?

Prisms are three dimensional figures that occupy space. They come in many shapes and sizes and are named by the shape of their base. Prisms have the following characteristics: 
  • A prism has two congruent bases that are parallel.
  • No curves
  • Prisms are named by the shape of the base. For example a prism with a triangle base is a triangular prism.  
  • The base of a prism can be any two parallel sides. If the shape does not have two parallel sides it is not a prism.
  • Volume of a prism equals Base Area x Height
  • A prism is a polyhedron, which is a solid with faces that are flat

The base of a prism can be any two parallel sides.

The edge is where the two faces intersect

The face is the flat surface of the prism

How do you find the surface area of a prism?

The video works the sample area of a prism problem below.

The formula for finding the surface area of a rectangular prism equals:​ 2* (length *width) + 2(length*height) + 2*(height * width) = surface area of a prism

Find the surface area of a rectangular prism with a length of 6 units, a height of 3 units and a width of 4 units.

Step 1.   Plug in the appropriate units in the formula
              2* (6*4) + 2(6*3) + 2( 3*4)
               (L*W)     ( L*H)    (H*W)
 
Step 2.    2*24 + 2*18 + 2*12
 
Step 3.    48+36+24 = 108 units squared   (surface area is always squared)

How do you find the surface area of a prism that is not rectangular?

The formula for finding the surface area of a non- rectangular prism equals:​

Surface Area = Lateral Area + 2 Base Areas

Lateral Area = P * h​

P = perimeter  h = height of prism  

The formula for finding the base area will vary according to the shape of the prism. 
Check here for a list of base area formulas
Find the surface area of a triangular prism with dimensions 16,12,10, and 20 cm. ( see picture)
Step 1. Find your lateral area. using P * h
           P = 16 + 20 + 12 = 48
           Multiply 48 x the prism height = 48 * 10 = 480 LA
Step 2. Find your base area. The base is a triangular base therefore use 1/2 base * height  1/2 (12) * 16 = 6 * 16 = 96 base area
 
You have two bases therefore multiply by 2  2 * 96 = 192 
 
Step 3. Add your lateral area and your base area for the total surface area
 
480 + 192 = 672 square centimeters

Video answer to surface area of a triangular prism problem