Question

what is the surface area of the trapezoidal prism? s.a. = 152 ft². expression can be used to find the surface area of the trapezoidal prism? 6·3 + 6·4 + 6·5 + 6·8 + 23·4 + 1/2(3·4)

Explanation:

Step1: Identify surface - area components

The surface area of a trapezoidal prism is the sum of the areas of its faces. There are two trapezoidal bases and four rectangular lateral faces.
The areas of the rectangular faces are: $6\times3$, $6\times4$, $6\times5$, $6\times8$.
The area of a trapezoid is $A=\frac{1}{2}(b_1 + b_2)h$, and here for the trapezoidal bases with parallel - sides 3 and 5 and height 4, the area of one trapezoid is $\frac{1}{2}(3 + 5)\times4$, and for two trapezoids it is $2\times\frac{1}{2}(3\times4)$.

Step2: Calculate surface area formula

The surface - area formula for the trapezoidal prism is $SA=6\times3+6\times4+6\times5+6\times8 + 2\times\frac{1}{2}(3\times4)$.

Answer:

$SA = 6\times3+6\times4+6\times5+6\times8+2\times\frac{1}{2}(3\times4)$