What is the formula for the surface area of a rectangular prism?

The surface area of a rectangular prism is calculated by adding up the areas of all its faces. A rectangular prism has six faces: two faces for each dimension—length, width, and height.

To derive the formula, consider the areas of each pair of opposite faces:

• The area of the top and bottom faces, which each have dimensions length and width, contributes (2 \times (length \times width)).

• The area of the front and back faces, which each have dimensions length and height, contributes (2 \times (length \times height)).

• The area of the left and right faces, which each have dimensions width and height, contributes (2 \times (width \times height)).

When you add these areas together, the complete formula for the surface area becomes:

[

S.A. = 2(length \times width) + 2(length \times height) + 2(width \times height)

]

This succinctly captures the contributions of all faces to the total surface area, confirming that the correct answer is indeed the one that states this complete sum.