Question

a rectangular prism and its net are shown below. the top and bottom of the prism are shaded. (all lengths are in yards.) (a) find the following side lengths for the net. a = yd b = yd c = yd d = yd (b) use the net to find the lateral surface area of the prism. neither the top nor bottom is included. yd² (c) use the net to find the total surface area of the prism. yd²

Explanation:

Step1: Identify side - lengths from 3D shape

In a rectangular prism, for the net, if the dimensions of the prism are length $l = 9$, width $w=2$, and height $h = 5$.
$A$ corresponds to the length of the prism, so $A = 9$ yd.
$B$ corresponds to the height of the prism, so $B = 5$ yd.
$C$ corresponds to the width of the prism, so $C = 2$ yd.
$D$ corresponds to the width of the prism, so $D = 2$ yd.

Step2: Calculate lateral surface area

The lateral - surface area $LSA$ of a rectangular prism (excluding top and bottom) is given by the sum of the areas of the four side - faces. The formula is $LSA=2(lh + wh)$.
$LSA=2(9\times5+2\times5)=2(45 + 10)=2\times55 = 110$ yd².

Step3: Calculate total surface area

The total surface area $TSA$ of a rectangular prism is given by the formula $TSA = 2(lw+lh+wh)$.
$TSA=2(9\times2 + 9\times5+2\times5)=2(18 + 45+10)=2\times73 = 146$ yd².

Answer:

(a)
$A = 9$ yd
$B = 5$ yd
$C = 2$ yd
$D = 2$ yd
(b) $110$ yd²
(c) $146$ yd²