Question

a rectangular prism is shown below.
which diagram is a net for this prism?
what is the surface area of the rectangular prism?
______ square millimeters

Explanation:

Step1: Recall surface area formula

The surface area $SA$ of a rectangular prism with length $l$, width $w$, height $h$ is:
$$SA = 2(lw + lh + wh)$$

Step2: Assign given values

Let $l=16$ mm, $w=12$ mm, $h=7$ mm.

Step3: Calculate each face area sum

First compute each product:
$lw = 16\times12 = 192$, $lh = 16\times7 = 112$, $wh = 12\times7 = 84$
Sum: $192 + 112 + 84 = 388$

Step4: Compute total surface area

Multiply the sum by 2:
$SA = 2\times388 = 776$

A net of the rectangular prism must have 3 pairs of rectangles with dimensions (16×12), (16×7), and (12×7). The second diagram (right one) correctly includes these pairs of matching rectangles that can fold into the given prism, while the first diagram has mismatched side length pairings.

Answer:

776

For the net identification: