Definition:

A triangular prism is a polyhedron with two parallel triangular bases and three rectangular faces.

Formulas:

• Surface Area: The surface area of a triangular prism can be calculated using the formula:
  2 * base area of the triangle + perimeter of the triangle * height of the prism
• Volume: The volume of a triangular prism can be calculated using the formula:
  base area of the triangle * height of the prism

Example Problem:

Find the surface area and volume of a triangular prism with the following measurements:

• Base of the triangle: 5 cm
• Height of the triangle: 8 cm
• Height of the prism: 10 cm

Solution:

First, calculate the base area of the triangle:
base area = (1/2) * base * height
base area = (1/2) * 5 cm * 8 cm = 20 cm²

Then, find the perimeter of the triangle:
perimeter = 3 * base
perimeter = 3 * 5 cm = 15 cm

Now, calculate the surface area:
surface area = 2 * base area + perimeter * height of the prism
surface area = 2 * 20 cm² + 15 cm * 10 cm = 400 cm² + 150 cm² = 550 cm²

Finally, calculate the volume:
volume = base area * height of the prism
volume = 20 cm² * 10 cm = 200 cm³

Conclusion:

The surface area of the triangular prism is 550 cm² and the volume is 200 cm³.