Surface Area of Prisms

How to find the surface area and volume of prisms.

Theory:

A 'prism' is a solid figure with a uniform cross section. Here are some examples of prisms:

Rectangular based prism:

Circular based prism: (Cylinder)

Triangular based prism:

The surface area of any prism equals the sum of the areas of its faces, which include the floor, roof and walls. Because the floor and the roof of a prism have the same shape, the surface area can always be found as follows:

From now on we will call the 'floor' the 'base'. The height of the prism = 'H'.

The surface area of a prism = 2 × area of base + perimeter of base × H

The actual formula used to find the surface area will depend on the shape of the base of the prism.

For example:

Rectangular based prism Base shape: Rectangle, length 'L' and width 'W' Area of base: L × W Perimeter of base: 2(L+W) Surface area = 2LW + 2(L+W)H

Circular based prism Base shape: Circle, radius 'R' Area of base: pR² Perimeter of base: 2pR Surface area = 2pR² + 2pRH

Triangular based prism Base shape: Triangle: base 'b', height 'h', and sides S₁, S₂ and S₃ Area of base: ½b×h Perimeter of base: S₁+ S₂ + S₃ Surface area = bh + (S₁+ S₂ + S₃)H