The image you uploaded contains exercises related to the surface area of prisms ("Oberfläche des Prismas"). Let's break down the content and solve the problems step by step.

Exercise 1:

You are asked to calculate the surface area of the prisms. The general formula for the surface area of a prism is:

$O = 2 \cdot G + M$

Where:

• $G$ is the area of the base (Grundfläche),
• $M$ is the lateral surface area (Mantelfläche).

Part a:

A trapezoidal prism is given with the following dimensions:

• The trapezoid has parallel sides of lengths 6 cm and 8 cm,
• The height of the trapezoid is 5 cm,
• The depth (height of the prism) is 5.2 cm.

Let's calculate:

1. Base area $G$ (area of the trapezoid):

$G = \frac{(a + b) \cdot h}{2} = \frac{(6 \, \text{cm} + 8 \, \text{cm}) \cdot 5 \, \text{cm}}{2} = \frac{14 \cdot 5}{2} = 35 \, \text{cm}^2$

2. Lateral surface area $M$:

You have already calculated the total lateral surface area, which is $M = 72.64 \, \text{cm}^2$.

3. Total surface area $O$:

$O = 2 \cdot G + M = 2 \cdot 35 \, \text{cm}^2 + 72.64 \, \text{cm}^2 = 140 \, \text{cm}^2$

Part b:

A triangular prism with the following dimensions:

• Triangle base has height $8 \, \text{cm}$ and base length $5 \, \text{cm}$,
• The depth of the prism is $9.4 \, \text{cm}$.

1. Base area $G$ (area of the triangle):

$G = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 5 \, \text{cm} \cdot 8 \, \text{cm} = 20 \, \text{cm}^2$

2. Lateral surface area $M$:

$M = \text{Perimeter of the triangle} \cdot \text{depth}$ The perimeter of the triangle would be $5 \, \text{cm} + 8 \, \text{cm} + 9.4 \, \text{cm} = 22.4 \, \text{cm}$.

Thus:

$M = 22.4 \, \text{cm} \cdot 9.4 \, \text{cm} = 210.56 \, \text{cm}^2$

3. Total surface area $O$:

$O = 2 \cdot G + M = 2 \cdot 20 \, \text{cm}^2 + 210.56 \, \text{cm}^2 = 250.56 \, \text{cm}^2$

Exercise 2:

You are asked to calculate the minimum amount of cardboard (cm²) needed for packaging the objects shown in the images. Let's quickly outline the steps for solving these based on the shapes:

Part a:

This involves calculating the surface area of a trapezoidal package.

1. Trapezoid area calculation.
2. Surface area of the entire packaging (including the lateral surfaces).

Part b:

A triangular package, where you follow the same process of calculating surface area for all sides and lateral parts.

If you need more detailed steps or a specific breakdown of the second exercise, let me know!

Would you like more details on any part or further clarifications?

Related Questions:

1. How do you find the lateral surface area of any prism?
2. What are the key differences between triangular and trapezoidal prisms in surface area calculations?
3. How does the base shape affect the surface area formula?
4. How can you find the total surface area of more complex 3D shapes like pyramids?
5. How do real-world packaging problems use surface area calculations?

Tip:

Always verify units in surface area calculations to ensure they are consistent (e.g., cm² for all surface area values).