Surface Area of Rectangular Prism: Express in Terms of a, b, and c

The problem requires us to find the surface area of a rectangular prism in terms of $a$, $b$, and $c$. To find this, we use the standard formula for the surface area of a cuboid.

The surface area of a cuboid is given by:

$S = 2(ab + bc + ca)$

Explanation of the formula:

• Each face of the cuboid is a rectangle. There are three unique rectangles in a cuboid:
• Two faces with dimensions $a \times b$,
• Two faces with dimensions $b \times c$,
• Two faces with dimensions $c \times a$.

These three pairs of faces contribute to the total surface area as follows:

• Area of the two $a \times b$ faces: $2 \times (ab)$
• Area of the two $b \times c$ faces: $2 \times (bc)$
• Area of the two $c \times a$ faces: $2 \times (ca)$

Adding these areas together gives us the total surface area:

$S = 2ab + 2bc + 2ca$

This simplifies to $2(ab + bc + ca)$.

Given the choices, the correct expression for the surface area is $2ac + 2ab + 2bc$.