Question

what is the surface area of the trapezoidal prism? s.a. = ___ ft² which 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 the surface - area formula components

The surface area of a trapezoidal prism $SA$ is the sum of the areas of all its faces. The trapezoidal prism has two congruent trapezoidal bases and four rectangular lateral faces.
The formula for the area of a trapezoid is $A_{t}=\frac{1}{2}(b_1 + b_2)h$, and for a rectangle is $A_{r}=l\times w$.
The four rectangular faces have areas: $6\times3$, $6\times4$, $6\times5$, $6\times8$. The two trapezoidal bases have combined area $2\times\frac{1}{2}(3 + 5)\times4=2\times(3\times4 + 5\times4)\div2$.
We calculate the sum of the areas of the rectangular faces and the trapezoidal bases.

Step2: Calculate the sum of areas

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Answer:

$152$