Question

the figure shows a net of a rectangular prism.
area of rectangle
a = l·w
which expression can be used to find the surface area of the prism?
(20·8) + (20·3) + (8·3)
20·8·3
2(20·8) + 2(20·3) + 2(8·3)
2(20·8·3)
image of a rectangular prism net with dimensions 20 cm, 8 cm, 3 cm

Explanation:

Step1: Recall Surface Area Formula for Rectangular Prism

The surface area \( SA \) of a rectangular prism is given by \( SA = 2(lw + lh + wh) \), where \( l \), \( w \), and \( h \) are the length, width, and height respectively. From the net, we can identify the dimensions: \( l = 20 \) cm, \( w = 8 \) cm, \( h = 3 \) cm.

Step2: Expand the Formula

Substitute \( l = 20 \), \( w = 8 \), \( h = 3 \) into the formula:
\[

$$\begin{align*} SA&= 2(20 \cdot 8 + 20 \cdot 3 + 8 \cdot 3)\\ &= 2(20 \cdot 8) + 2(20 \cdot 3) + 2(8 \cdot 3) \end{align*}$$

\]
This matches the expression \( 2(20 \cdot 8) + 2(20 \cdot 3) + 2(8 \cdot 3) \) (or \( 2(20 \cdot 8)+2(20 \cdot 3)+2(8 \cdot 3) \) as in the options).

Answer:

The expression \( 2(20 \cdot 8) + 2(20 \cdot 3) + 2(8 \cdot 3) \) (the third option in the list: \( 2(20 \cdot 8)+2(20 \cdot 3)+2(8 \cdot 3) \)) can be used to find the surface area of the prism.