To calculate the surface area of the prism, we need to find the area of all the faces (2 trapezium cross-sections and the rectangular sides). Here's a step-by-step calculation:

Step 1: Calculate the area of the trapezium cross-section

The area $A$ of a trapezium is given by:

$A = \frac{1}{2} \times (a + b) \times h$

Here:

• $a = 16 \, \text{cm}$ (bottom base)
• $b = 11 \, \text{cm}$ (top base)
• $h = 6 \, \text{cm}$ (height)

$A = \frac{1}{2} \times (16 + 11) \times 6 = \frac{1}{2} \times 27 \times 6 = 81 \, \text{cm}^2$

Thus, the area of one trapezium is $81 \, \text{cm}^2$.

Since there are two identical trapezium cross-sections:

$\text{Total area of trapezium faces} = 2 \times 81 = 162 \, \text{cm}^2$

Step 2: Calculate the areas of the rectangular sides

The prism has three rectangular sides:

1. Side 1 (rectangular face connecting $16 \, \text{cm}$ and depth $7 \, \text{cm}$): $A_1 = 16 \times 7 = 112 \, \text{cm}^2$

2. Side 2 (rectangular face connecting $11 \, \text{cm}$ and depth $7 \, \text{cm}$): $A_2 = 11 \times 7 = 77 \, \text{cm}^2$

3. Side 3 (rectangular face connecting slant $17 \, \text{cm}$ and depth $7 \, \text{cm}$): $A_3 = 17 \times 7 = 119 \, \text{cm}^2$

Step 3: Add all areas

Now, summing up the areas of all the faces:

$\text{Total surface area} = 162 + 112 + 77 + 119 = 470 \, \text{cm}^2$

Final Answer:

The surface area of the prism is:

$\boxed{470 \, \text{cm}^2}$

Let me know if you want further clarification or details.

Follow-up Questions:

1. How do you calculate the area of a trapezium for irregular shapes?
2. Why do slanted faces require their exact lengths in prism surface calculations?
3. What other 3D shapes involve trapezium cross-sections in their surface area calculations?
4. How would the answer change if the depth of the prism increased?
5. How do units impact calculations when dimensions are given in mixed units?

Tip:

Always label and organize dimensions clearly in geometry problems to avoid confusion when dealing with multiple faces or shapes.