Question

which expression can be used to find the surface area of the trapezoidal prism? 0·3 + 0·4 + 0·5 + 0·8 + 21/2(3·4) what is the surface area of the trapezoidal prism? s.a. = ft² s.a. = 0·3 + 0·4 + 0·5 + 0·8 + 21/2(3·4) = 18 + 24 + 30 + 48 + 36

Explanation:

Step1: Recall surface - area formula for trapezoidal prism

The surface area of a trapezoidal prism $SA$ is the sum of the areas of all its faces. The formula is $SA =$ (sum of areas of trapezoidal bases)+(sum of areas of rectangular lateral - faces). If the trapezoid has bases $b_1$ and $b_2$, height $h$ of the trapezoid, and the length of the prism is $l$, and the non - parallel sides of the trapezoid are $s_1$ and $s_2$. The area of a trapezoid $A_{t}=\frac{1}{2}(b_1 + b_2)h$, and the areas of the rectangular faces are $l\times b_1$, $l\times b_2$, $l\times s_1$, $l\times s_2$.
In the given expression $SA=6\times3 + 6\times4+6\times5 + 6\times8+2[\frac{1}{2}(3\times4)]$. Here, assume the dimensions of the trapezoidal prism: the lengths of the rectangles' sides are likely related to the edges of the prism. The terms $6\times3$, $6\times4$, $6\times5$, $6\times8$ are the areas of the rectangular faces (where 6 might be the length of the prism), and $2[\frac{1}{2}(3\times4)]$ is the sum of the areas of the two trapezoidal bases (assuming the trapezoid has relevant dimensions 3 and 4).

Step2: Calculate the value

First, calculate each product:
$6\times3 = 18$, $6\times4 = 24$, $6\times5 = 30$, $6\times8 = 48$, and $2[\frac{1}{2}(3\times4)]=12$.
Then, sum them up: $SA=18 + 24+30 + 48+12$.
$18+24=42$, $42 + 30=72$, $72+48 = 120$, $120+12=132$.

Answer:

$132$