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To solve the problem of finding the surface area of the prism, we will follow these steps:

### Given Information
- The prism has two faces that are regular hexagons, each with an area of \( 23 \, \text{cm}^2 \).
- The height of the prism (distance between the two hexagonal faces) is \( 9 \, \text{cm} \).
- The side length of the hexagonal base is \( 3 \, \text{cm} \).

### Step 1: Find the area of the two hexagonal bases
The prism has two identical hexagonal faces. Given that each hexagonal face has an area of \( 23 \, \text{cm}^2 \), the total area of both bases is:
\[
2 \times 23 = 46 \, \text{cm}^2
\]

### Step 2: Find the area of the rectangular faces (lateral surface area)
The prism has six rectangular faces, one for each side of the hexagon. Each of these faces has a width equal to the side length of the hexagon (\( 3 \, \text{cm} \)) and a height equal to the height of the prism (\( 9 \, \text{cm} \)).

The area of one rectangular face is:
\[
3 \, \text{cm} \times 9 \, \text{cm} = 27 \, \text{cm}^2
\]

Since there are 6 such faces, the total lateral surface area is:
\[
6 \times 27 = 162 \, \text{cm}^2
\]

### Step 3: Calculate the total surface area of the prism
The total surface area is the sum of the areas of the two hexagonal faces and the lateral surface area:
\[
46 \, \text{cm}^2 + 162 \, \text{cm}^2 = 208 \, \text{cm}^2
\]

### Final Answer
The surface area of the prism is:
\[
\boxed{208 \, \text{cm}^2}
\]

Would you like any further details or have any questions?

Here are 5 related questions that expand on this concept:
1. How would the surface area change if the height of the prism were doubled?
2. What would be the volume of this prism?
3. How do you find the surface area of a prism with different polygonal bases?
4. How would the calculation change if the side length of the hexagon changed?
5. How do the properties of regular polygons simplify surface area calculations?

**Tip:** Always break down complex 3D problems into simpler parts (base areas and lateral surfaces) for easier calculations.

The prism below has two faces that are regular hexagons. Each hexagonal face has an area of 23 cm². What is the surface area of the prism? Remember to give the correct units.

Learn how to calculate the surface area of a prism with regular hexagonal faces. This problem involves calculating the areas of two hexagonal bases and the lateral rectangular faces. Suitable for students in Grades 8-10.

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