Question

which expression can be used to find the surface area of the trapezoidal prism? 5 2 + 5 3+5 4 + 5 7+2(2 3+1/2(2 4)) what is the surface area of the trapezoidal prism? sa = cm²

Explanation:

Step1: Analyze the faces of the prism

The trapezoidal prism has two congruent trapezoidal faces and four rectangular faces.
The area of a trapezoid is $A_{t}=\frac{1}{2}(a + b)h$, where $a$ and $b$ are the parallel - sides and $h$ is the height of the trapezoid. Here, for the trapezoid, $a = 3$, $b = 4$, and $h = 2$. The area of one trapezoid is $A_{t}=\frac{1}{2}(3 + 4)\times2=7$. The area of two trapezoids is $2\times7 = 14$.
The four rectangular faces have dimensions:

• One rectangle with dimensions $2\times7$, its area $A_{1}=2\times7 = 14$.
• One rectangle with dimensions $3\times7$, its area $A_{2}=3\times7 = 21$.
• One rectangle with dimensions $4\times7$, its area $A_{3}=4\times7 = 28$.
• One rectangle with dimensions $5\times7$, its area $A_{4}=5\times7 = 35$.

The surface - area formula for the trapezoidal prism $SA=2\times\frac{1}{2}(3 + 4)\times2+2\times7+3\times7+4\times7+5\times7$.

Step2: Calculate the surface area

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Answer:

$112$