To find the volume of the structure shown in the image, which appears to be a combination of a rectangular prism and a triangular prism, we can break it down into two parts and calculate their volumes separately.

Step 1: Volume of the Rectangular Prism

The rectangular prism forms the bottom part of the structure.

• Base dimensions: $12 \, \text{m} \times 3 \, \text{m}$
• Height: $10 \, \text{m}$

The volume of the rectangular prism is:

$V_{\text{rectangular}} = \text{Base Area} \times \text{Height} = (12 \times 3) \times 10 = 36 \times 10 = 360 \, \text{m}^3$

Step 2: Volume of the Triangular Prism

The triangular prism forms the roof part of the structure.

• Base of the triangle: $12 \, \text{m}$
• Height of the triangle: $2 \, \text{m}$
• Length of the prism (same as the height of the rectangular prism): $10 \, \text{m}$

First, calculate the area of the triangular base:

$\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 \times 2 = 12 \, \text{m}^2$

Now, calculate the volume of the triangular prism:

$V_{\text{triangular}} = \text{Area of Triangle} \times \text{Length} = 12 \times 10 = 120 \, \text{m}^3$

Step 3: Total Volume

Add the volumes of the rectangular and triangular prisms together:

$\text{Total Volume} = V_{\text{rectangular}} + V_{\text{triangular}} = 360 + 120 = 480 \, \text{m}^3$

Thus, the total volume of the structure is $480 \, \text{m}^3$.

Would you like more details or have any other questions?

Here are some related questions:

1. How would you calculate the surface area of this structure?
2. What is the significance of the shape of the roof in real-world applications?
3. How does the volume change if the height of the triangular prism is increased?
4. How would you calculate the total perimeter of the base of this structure?
5. How does changing the dimensions of the base affect the overall volume?

Tip: When dealing with composite shapes, always break them down into simpler components to make calculations easier.