Question

(a) find the following side lengths for the net.
$a = 9$ yd
$b = 2$ yd
$c = 5$ yd
$d = 9$ yd
(b) use the net to find the surface area of the prism.
$\square$ yd$^2$

Explanation:

Step1: Match net sides to prism

From the prism:

• $A$ matches the prism's length: $A=9$ yd
• $B$ matches the prism's height: $B=2$ yd
• $C$ matches the prism's width: $C=5$ yd
• $D$ matches the prism's width: $D=5$ yd

Step2: Calculate area of each face type

• Area of 2 large rectangles: $2\times(A\times C) = 2\times(9\times5)$
• Area of 2 medium rectangles: $2\times(A\times B) = 2\times(9\times2)$
• Area of 2 small rectangles: $2\times(B\times C) = 2\times(2\times5)$

Step3: Compute total surface area

Add all face areas:

$$\begin{align*} \text{Total Area} &= 2(9\times5) + 2(9\times2) + 2(2\times5)\\ &= 2(45) + 2(18) + 2(10)\\ &= 90 + 36 + 20 \end{align*}$$

Answer:

(a)
$A=9$ yd, $B=2$ yd, $C=5$ yd, $D=5$ yd
(b)
$146$ yd²