https://file.aiquickdraw.com/mathbot/file/17295458643355iuf1okt.jpg

Calculate the surface area of the figure.

To calculate the surface area of the given figure, which appears to be a triangular prism, we need to find the areas of all its faces.

### Step 1: Identify the dimensions
- **Base of the triangle** (one face of the prism): 12 m
- **Height of the triangle**: 5 m
- **Length of the prism** (distance between the triangular faces): 15 m
- **Sides of the triangle**: 12 m, 13 m, 5 m

### Step 2: Calculate the area of the two triangular faces
The area of one triangle (using the base and height) is given by:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \, m \times 5 \, m = 30 \, m^2
\]
Since the prism has two triangular faces:
\[
\text{Total area of triangular faces} = 2 \times 30 \, m^2 = 60 \, m^2
\]

### Step 3: Calculate the area of the three rectangular faces
Each rectangular face is formed by one of the sides of the triangle and the length of the prism (15 m).
- The area of the rectangle formed by the side of 12 m:
\[
12 \, m \times 15 \, m = 180 \, m^2
\]
- The area of the rectangle formed by the side of 13 m:
\[
13 \, m \times 15 \, m = 195 \, m^2
\]
- The area of the rectangle formed by the side of 5 m:
\[
5 \, m \times 15 \, m = 75 \, m^2
\]

### Step 4: Add the areas of all the faces
Now, add the areas of the triangular faces and the rectangular faces:
\[
\text{Total surface area} = 60 \, m^2 + 180 \, m^2 + 195 \, m^2 + 75 \, m^2 = 510 \, m^2
\]

### Final Answer:
The surface area of the triangular prism is **510 square meters**.

Let me know if you need any further explanation!

Here are 5 related questions:
1. How do you calculate the surface area of a rectangular prism?
2. What is the volume of this triangular prism?
3. How do you find the perimeter of a triangle given its sides?
4. How do you calculate the surface area of a cylinder?
5. Can you find the lateral surface area of a prism without the bases?

Tip: Always double-check the units when calculating surface areas to ensure consistency throughout your solution!

Learn how to calculate the surface area of a triangular prism with a base of 12 meters, height of 5 meters, and sides of 13 meters. The problem involves calculating the areas of triangular and rectangular faces. Suitable for students in Grades 7-9.

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