Question

a rectangular prism and its net are shown below. (all lengths are in yards.) (a) find the following side lengths for the net. a = \boxed{} yd b = \boxed{} yd c = \boxed{} yd d = \boxed{} yd (b) use the net to find the surface area of the prism. \boxed{} yd²

Explanation:

Step1: Match prism sides to net

From the rectangular prism, the dimensions are 8 yd, 11 yd, and 8 yd.

• $A$ matches the height of the prism: $A = 8$
• $B$ matches the length of the prism: $B = 11$
• $C$ matches the height of the prism: $C = 8$
• $D$ matches the length of the prism: $D = 11$

Step2: Calculate area of each face

The net has 6 faces: 2 pairs of equal rectangles.

• Area of first pair: $2 \times (8 \times 11) = 2 \times 88 = 176$
• Area of second pair: $2 \times (8 \times 8) = 2 \times 64 = 128$
• Area of third pair: $2 \times (8 \times 11) = 2 \times 88 = 176$

Step3: Sum all face areas

Add the areas of all faces to get surface area:
$\text{Surface Area} = 176 + 128 + 176$

Answer:

(a)
$A = 8$ yd
$B = 11$ yd
$C = 8$ yd
$D = 11$ yd

(b)
$480$ yd$^2$