Question

which expression can be used to find the surface area of the trapezoidal prism? area of rectangle a = l·w area of triangle a = 1/2(b·h) 6·3 + 6·4 + 6·5 + 6·8 + 21/2(3·4) 6·3 + 6·4 + 6·5 + 6·8 + 3·4 + 1/2(3·4) 6·3 + 6·4 + 6·5 + 23·4 + 1/2(3·4) 6·3 + 6·4 + 6·5 + 3·4 + 1/2(3·4)

Explanation:

Step1: Recall surface - area formula for prism

The surface area of a prism \(SA=2B + Ph\), where \(B\) is the area of the base, \(P\) is the perimeter of the base, and \(h\) is the height of the prism. For a trapezoidal prism, the base is a trapezoid. The area of a trapezoid \(A=\frac{1}{2}(b_1 + b_2)h\) (not relevant here as we can also calculate by summing areas of faces). The trapezoidal prism has two trapezoid bases and three rectangular lateral faces.

Step2: Analyze the rectangular faces

The three rectangular faces have areas: \(6\times3\), \(6\times4\), \(6\times5\). The two trapezoid bases have combined area equivalent to \(2\times\frac{1}{2}(3\times4)\) (assuming the trapezoid bases have parallel - side lengths and height such that the area formula simplifies this way). The surface - area formula for this trapezoidal prism is the sum of the areas of all its faces, which is \(6\times3+6\times4 + 6\times5+2\times\frac{1}{2}(3\times4)\).

Answer:

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