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

To find the total surface area of the prism, we need to consider both the lateral surface area and the area of the two bases.

### Step 1: Identify Given Information
- The total lateral surface area of the prism \( A_{\text{lateral}} \) 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: Calculate the Total Surface Area
The total surface area \( A_{\text{total}} \) of the prism is the sum of the lateral surface area and the areas of the two bases:
\[
A_{\text{total}} = A_{\text{lateral}} + 2 \times A_{\text{base}}
\]
Substituting the given values:
\[
A_{\text{total}} = 100 \, \text{cm}^2 + 2 \times 25 \, \text{cm}^2
\]
\[
A_{\text{total}} = 100 \, \text{cm}^2 + 50 \, \text{cm}^2
\]
\[
A_{\text{total}} = 150 \, \text{cm}^2
\]

### Final Answer
The total surface area of the prism is \( 150 \, \text{cm}^2 \).

Would you like any details or have any questions about the solution? Here are five related questions:

1. What is the formula for the lateral surface area of a prism?
2. How does the height of the prism relate to its lateral surface area?
3. Can the base of the prism be any shape, and how does that affect the total surface area?
4. What is the total surface area if the base area of the prism is doubled?
5. How does the surface area change if the height of the prism is doubled?

**Tip:** Remember, the total surface area of a prism always includes both the lateral surface area and the areas of all bases.

Learn how to calculate the total surface area of a prism when given the lateral surface area and base area. This problem involves understanding the geometry of prisms and applying the surface area formula. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation