Question

which expression can be used to find the surface area of the trapezoidal prism? 6·3 + 6·4 + 6·5 + 6·8 + 2\frac{1}{2}(3·4), 6·3 + 6·4 + 6·5 + 6·8 + 3·4 + \frac{1}{2}(3·4), 6·3 + 6·4 + 6·5 + 23·4 + \frac{1}{2}(3·4), 6·3 + 6·4 + 6·5 + 3·4 + \frac{1}{2}(3·4). area of rectangle a = l·w. area of triangle a = \frac{1}{2}(b·h)

Explanation:

Step1: Recall surface - area formula for prism

The surface area of a prism $SA$ is the sum of the areas of all its faces. For a trapezoidal prism, it is the sum of the areas of the two trapezoidal bases and the areas of the three rectangular lateral faces.

Step2: Analyze the areas of rectangular faces

The dimensions of the rectangular faces are likely related to the side - lengths of the trapezoid and the height of the prism. If the lengths of the parallel sides of the trapezoid are $a$ and $b$, the height of the trapezoid is $h_t$, and the height of the prism is $h_p$. The areas of the rectangular faces can be found using the formula for the area of a rectangle $A = l\times w$. The areas of the three rectangular faces with dimensions related to the trapezoid's sides and the prism's height are likely $6\times3$, $6\times4$, and $6\times5$ (assuming 6 is the height of the prism and 3, 4, 5 are side - lengths related to the trapezoid).

Step3: Analyze the area of trapezoidal bases

The area of a trapezoid is $A=\frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height of the trapezoid. Here, if the relevant dimensions of the trapezoid are 3 and 4 (parallel sides) and some height related to the trapezoid, and since there are two trapezoidal bases, the combined area of the two trapezoidal bases is $2\times\frac{1}{2}(3\times4)$.

Step4: Form the surface - area expression

The surface area of the trapezoidal prism is the sum of the areas of the three rectangular faces and the two trapezoidal bases. So the expression is $6\times3+6\times4 + 6\times5+2\times\frac{1}{2}(3\times4)$.

Answer:

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