https://file.aiquickdraw.com/mathbot/file/17254162413052u7mlngc.jpg

from PIL import Image
from pytesseract import image_to_string

# Load the image from the provided path
image_path = "/mnt/data/17254162413052u7mlngc.jpg"
img = Image.open(image_path)

# Extract text from the image
extracted_text = image_to_string(img)
extracted_textIt seems that the text extraction didn't fully capture the necessary details. I'll manually analyze the image to solve the problem.

### Analysis of the Image
The image shows a right triangular prism with its net displayed alongside it. The net consists of several parts:
- Two triangular faces.
- Three rectangular faces.

The problem asks us to:
1. Find the side lengths for the net.
2. Use the net to find the surface area of the prism.

### Step 1: Identify the Side Lengths
Given in the image:
- The triangular face has sides labeled 3 mm, 4 mm, and 5 mm (this is a right triangle).
- The height of the prism (which is also the length of the rectangle connected to the hypotenuse) is 15 mm.

The net's dimensions:
- A: Length of the rectangle adjacent to the side 3 mm.
- B: Length of the rectangle adjacent to the side 4 mm.
- C: Length of the rectangle adjacent to the hypotenuse 5 mm.
- D: Height of the prism (length of the rectangles) = 15 mm.

**Answers:**
- A = 3 mm
- B = 4 mm
- C = 5 mm
- D = 15 mm

### Step 2: Calculate the Surface Area
The surface area is the sum of the areas of all faces.

#### Triangular Faces:
Each triangular face has an area:
\[
\text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 4 = 6 \text{ mm}^2
\]
Since there are two triangular faces:
\[
\text{Total area of triangles} = 2 \times 6 = 12 \text{ mm}^2
\]

#### Rectangular Faces:
There are three rectangular faces:
1. \( 3 \times 15 = 45 \text{ mm}^2 \)
2. \( 4 \times 15 = 60 \text{ mm}^2 \)
3. \( 5 \times 15 = 75 \text{ mm}^2 \)

Adding these:
\[
\text{Total area of rectangles} = 45 + 60 + 75 = 180 \text{ mm}^2
\]

#### Total Surface Area:
\[
\text{Total Surface Area} = 12 + 180 = 192 \text{ mm}^2
\]

### Final Answers:
- (a) Side lengths: \( A = 3 \) mm, \( B = 4 \) mm, \( C = 5 \) mm, \( D = 15 \) mm.
- (b) Surface area: \( 192 \text{ mm}^2 \).

Would you like further details on any part? 

Here are 5 additional related questions:
1. How would the surface area change if the height of the prism doubled?
2. What is the volume of the triangular prism?
3. How would you find the surface area if the prism were a rectangular prism instead?
4. How does the Pythagorean theorem apply to the right triangle in the prism's net?
5. If the prism's height were halved, how would that affect the surface area?

**Tip:** Always double-check your work by verifying each dimension against the original diagram.

Solve the problem involving the right triangular prism and its net as shown in the image.

Learn how to calculate the surface area of a right triangular prism using its net diagram. This problem covers key geometric concepts including the surface area of prisms, right triangles, and the application of the Pythagorean theorem. Suitable for students in Grades 7-9.

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