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 centimeters

Explanation:

Step1: Identify prism dimensions

Length $l=20\ \text{cm}$, width $w=14\ \text{cm}$, height $h=9\ \text{cm}$

Step2: Match net to dimensions

A net for a rectangular prism must have 3 pairs of rectangles with areas $l\times w$, $l\times h$, $w\times h$. The second diagram has pairs: $20\times14$, $20\times9$, $14\times9$, which matches the prism's dimensions.

Step3: Calculate surface area

Use formula $SA=2(lw+lh+wh)$

$$\begin{align*} SA&=2((20\times14)+(20\times9)+(14\times9))\\ &=2(280+180+126)\\ &=2\times586 \end{align*}$$

Answer:

1. Correct net: The second diagram (right diagram with rectangles of 20×14, 20×9, 14×9 dimensions)
2. Surface area: $1172$ square centimeters