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# 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

480 + 192 = 672 square centimeters