Surface Area of a Rectangular Prism: Express in Terms of Variable 'a' (5×1×a)

To solve this problem, we must find the surface area of the rectangular prism with given dimensions $1$, $5$, and $a$.

The formula for the surface area $S$ of a rectangular prism with length $l$, width $w$, and height $h$ is:

$S = 2(lw + lh + wh)$

For this prism, let's identify the dimensions:

• Length ($l$) = 1
• Width ($w$) = 5
• Height ($h$) = a

Now, substitute these dimensions into the surface area formula:

$S = 2(1 \times 5 + 1 \times a + 5 \times a)$

Simplify the expression inside the parentheses:

$S = 2(5 + a + 5a)$

Combine the terms:

$S = 2(5 + 6a)$

Multiply through by 2:

$S = 10 + 12a$

Thus, the surface area of the rectangular prism expressed in terms of $a$ is $12a + 10$.