Given that the total surface area of a prism is 100 cm2 and the base area of the prism is 25 cm2. Find the total area of all lateral faces of a prism

To find the total area of all lateral faces of the prism, we need to use the relationship between the total surface area, the lateral surface area, and the area of the bases.

### Step 1: Identify Given Information
- The total surface area of the prism \( A_{\text{total}} \) is given as \( 100 \, \text{cm}^2 \).
- The base area of the prism \( A_{\text{base}} \) is given as \( 25 \, \text{cm}^2 \).

### Step 2: Express the Total Surface Area
The total surface area \( A_{\text{total}} \) is the sum of the lateral surface area \( A_{\text{lateral}} \) and the areas of the two bases:
\[
A_{\text{total}} = A_{\text{lateral}} + 2 \times A_{\text{base}}
\]
We need to solve for the lateral surface area \( A_{\text{lateral}} \).

### Step 3: Solve for the Lateral Surface Area
Substitute the given values into the formula:
\[
100 \, \text{cm}^2 = A_{\text{lateral}} + 2 \times 25 \, \text{cm}^2
\]
\[
100 \, \text{cm}^2 = A_{\text{lateral}} + 50 \, \text{cm}^2
\]
\[
A_{\text{lateral}} = 100 \, \text{cm}^2 - 50 \, \text{cm}^2
\]
\[
A_{\text{lateral}} = 50 \, \text{cm}^2
\]

### Final Answer
The total area of all lateral faces of the prism is \( 50 \, \text{cm}^2 \).

Would you like any more details or have any questions? Here are five related questions:

1. How do you calculate the lateral surface area if you know the height of the prism?
2. What would the lateral surface area be if the base area was increased by 10 cm²?
3. How does the number of sides of the base affect the lateral surface area?
4. Can the lateral surface area ever be larger than the total surface area?
5. How would you find the lateral surface area if the total surface area is unknown?

**Tip:** When solving for surface areas, always remember to account for all faces, including bases and lateral faces.

Learn how to calculate the total area of all lateral faces of a prism given its total surface area and base area. This problem involves using the formula for the lateral surface area of a prism and understanding geometric principles. Suitable for students in Grades 7-9.

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