The prism should be 8 cm high. Calculate the area of the prism with the base face in the figure (data in cm).

To calculate the area of a prism, we need to determine which areas you're referring to. A prism has three main surface areas:

1. The **lateral surface area** (sum of the areas of the rectangular faces).
2. The **base area** (the area of one of the two congruent bases).
3. The **total surface area**, which is the sum of the lateral surface area and the areas of both bases.

The formula for the **lateral surface area** \( A_{\text{lateral}} \) of a prism is:
\[
A_{\text{lateral}} = \text{perimeter of the base} \times \text{height}
\]

The **total surface area** \( A_{\text{total}} \) of a prism is:
\[
A_{\text{total}} = 2 \times \text{base area} + \text{lateral surface area}
\]

To proceed, I will need:
1. The shape and dimensions of the base face (whether it's a triangle, rectangle, etc.).
2. The perimeter and area of the base, or enough data to calculate these.

If you have a figure or specific base measurements (length, width, etc.), feel free to upload it, and I can provide a more precise calculation.

Would you like to upload the base figure, or share more details about its dimensions?

### Relative Questions:
1. Do you have the exact shape of the base of the prism?
2. What are the dimensions of the base face?
3. Are you looking for the lateral or total surface area?
4. Have you calculated the base area before, or should we work through that as well?
5. Is the prism right or oblique?

### Tip:
For prisms, the base shape plays a critical role in determining both the lateral and total surface areas, so always make sure the dimensions of the base are clearly understood.

Learn how to calculate the surface area of a prism with a height of 8 cm, using key geometric formulas like lateral surface area and total surface area. This problem is suitable for students in Grades 8-10 and involves calculating the perimeter and base area of the prism.

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