To solve for the surface area of the triangular prism, let's break it down step-by-step using the measurements from the net shown in the image.

Given Information

1. Triangular Faces: Two identical triangular faces with a base of 10 m and a height of 12 m.
2. Rectangular Faces: Three rectangular faces with lengths given:
   • One face with dimensions 15 m by 25 m.
   • Another with dimensions 10 m by 25 m.
   • Another with dimensions 20 m by 25 m.

Step 1: Calculate the Area of Each Triangular Face

The area of a triangle is calculated by: $\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ For each triangular face: $\text{Area} = \frac{1}{2} \times 10 \, \text{m} \times 12 \, \text{m} = 60 \, \text{m}^2$ Since there are two triangular faces: $\text{Total area of triangles} = 2 \times 60 \, \text{m}^2 = 120 \, \text{m}^2$

Step 2: Calculate the Area of Each Rectangular Face

1. First rectangle: $15 \, \text{m} \times 25 \, \text{m} = 375 \, \text{m}^2$
2. Second rectangle: $10 \, \text{m} \times 25 \, \text{m} = 250 \, \text{m}^2$
3. Third rectangle: $20 \, \text{m} \times 25 \, \text{m} = 500 \, \text{m}^2$

Step 3: Add All the Areas Together

$\text{Total Surface Area} = \text{Area of triangles} + \text{Area of rectangles}$ $= 120 \, \text{m}^2 + 375 \, \text{m}^2 + 250 \, \text{m}^2 + 500 \, \text{m}^2$ $= 1245 \, \text{m}^2$

Answer

The surface area of the prism is: $\boxed{1245 \, \text{m}^2}$

Would you like more details on any of these steps?

Related Questions

1. How would you find the volume of this triangular prism?
2. If the height of the prism changes, how would that affect the surface area?
3. What is the difference between lateral surface area and total surface area?
4. How can we use nets to find surface areas for other prisms, like rectangular prisms?
5. Why do we multiply the triangular face area by two in this case?

Tip

When calculating the surface area of prisms, always identify all unique faces and confirm if they repeat, as this simplifies calculations.