Find the surface area of a
rectangular prism with side lengths 𝑥, 11𝑦, and 15𝑧.
We begin by sketching the
rectangular prism with the given dimensions. Next, we recall that the surface
area of a rectangular prism is the sum of the areas of each of its faces. Since a rectangular prism has
rectangular faces, these areas will be given by the products of pairs of its side
Firstly, we have 𝑥 multiplied by
11𝑦, which is equal to 11𝑥𝑦. Next, we have 𝑥 multiplied by
15𝑧, which is equal to 15𝑥𝑧. Then, we have 11𝑦 multiplied by
15𝑧, which is equal to 165𝑦𝑧.
Since opposite faces on a
rectangular prism have equal areas, the surface area of this rectangular prism will
be the sum of double each of these expressions. This is equal to two multiplied by
11𝑥𝑦 plus two multiplied by 15𝑥𝑧 plus two multiplied by 165𝑦𝑧. Simplifying our expression gives us
22𝑥𝑦 plus 30𝑥𝑧 plus 330𝑦𝑧.
Hence, the surface area of the
rectangular prism is given by the expression 22𝑥𝑦 plus 330𝑦𝑧 plus 30𝑥𝑧.