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The worksheet contains geometry problems involving prisms, asking for the total surface area and volume of each solid based on their given measurements. Here's a step-by-step breakdown of what needs to be done:

### Tasks from the Worksheet:
1. **Total Surface Area**:
   - **Formula**: \( \text{Area Total} = \text{Area Lateral} + 2 \times \text{Area de la Base} \)
   - For each prism, calculate the perimeter of the base, the lateral surface area, and the base area based on the shape.

2. **Volume**:
   - **Formula**: \( \text{Volume} = \text{Area de la Base} \times \text{Altura} \)

### Shapes and Given Dimensions:
1. **Prism 1**:
   - Base: Square with side length 13 cm.
   - Height of the prism: 10 cm.

2. **Prism 2**:
   - Base: Hexagon with side length 8 cm.
   - Height of the prism: 5 cm.

3. **Prism 3**:
   - Base: Rectangular with dimensions 4 cm and 9 cm.
   - Height of the prism: 10 cm.

### Next Steps for Calculation:
1. **Calculate the perimeter** for the base of each solid.
2. **Calculate the lateral surface area** by multiplying the perimeter of the base by the height of the prism.
3. **Calculate the base area** (depends on the shape: square, hexagon, or rectangle).
4. **Calculate the total surface area** using the formula.
5. **Calculate the volume** using the formula for each solid.

Would you like me to calculate these values for each prism in detail?

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### Related Questions:
1. How do you find the lateral area of a prism with any polygonal base?
2. What are the differences in calculating the area of a square, hexagon, and rectangle?
3. How does the shape of the base affect the volume of the prism?
4. Can you derive the total surface area formula for any type of prism?
5. What are the real-world applications of these surface area and volume calculations?

#### Tip:
For a regular polygon (like a hexagon), the area can be calculated using the formula \( \frac{3\sqrt{3}}{2} \times \text{side}^2 \) for regular hexagons.

Solve geometric problems involving prisms, asking for the total surface area and volume of each solid based on their given measurements.

Explore detailed solutions for calculating the total surface area and volume of various prisms based on their dimensions. This guide provides formulas, step-by-step processes, and answers for educational purposes, suitable for students in Grades 9-12.

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