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Rule

Surface Area of a Rectangular Prism

Consider a rectangular prism with a height h, base area B, and base perimeter P.

The surface area of the rectangular prism can be found using the following formula.

SA=2(wl+hl+hw)

Proof

Recall that the surface area of a prism is the sum of the lateral area and the combined areas of the two identical bases. SA=Ph+2B Here P is the perimeter of the base, h is the height of the prism, and B is area of one base. The base of a rectangular prism is a rectangle, so its area is the product of its width and length. B=wl The perimeter of a rectangle can be found using the following formula. P=2(w+l) Now the expressions for P and B can be substituted into the formula presented in the beginning and the whole expression simplified.

SA=Ph+2B

SubstituteII

P= 2(w+l), B= wl

SA= 2(w+l)h+2 wl

Distr

Distribute h

SA=2(wh+l h)+2wl

FactorOut

Factor out 2

SA=2(wh+l h+wl)

This process results in the formula for the surface area of a rectangular prism.

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