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
