Triangular Prism

A triangular prism is a three-dimensional shape with two triangular bases and three rectangular faces. The two triangular bases are connected by three rectangular faces, making it a type of prism.

Properties of a Triangular Prism:

1. It has 6 faces: 2 triangular bases and 3 rectangular faces.
2. It has 9 edges: 3 on each triangular base and 3 connecting the bases.
3. It has 5 vertices: 6 vertices on each triangular base and 3 connecting the bases.
4. The two triangular bases are parallel to each other.

Formulas for a Triangular Prism:

To find the surface area and volume of a triangular prism, you can use the following formulas:

Surface Area = 2 * (Area of base) + (Perimeter of base) * (Height of prism)

Volume = (Area of base) * (Height of prism)

Example Problem:

Calculate the surface area and volume of a triangular prism with the following dimensions:

• Base: equilateral triangle with side length 5 cm
• Height of prism: 8 cm

Solution:

First, calculate the area of the base:
Area of equilateral triangle = (sqrt(3) / 4) * side length² = (sqrt(3) / 4) * 5² = (sqrt(3) / 4) * 25 = 25sqrt(3) / 4 square cm

Now, calculate the perimeter of the base:
Perimeter of equilateral triangle = 3 * side length = 3 * 5 = 15 cm

Surface Area = 2 * (25sqrt(3) / 4) + 15 * 8 = 25sqrt(3) + 120 square cm

Volume = (25sqrt(3) / 4) * 8 = 50sqrt(3) cubic cm

Study Guide:

To master the concept of a triangular prism, it's important to understand the following key points:

1. Identifying the faces, edges, and vertices of a triangular prism.
2. Understanding the formulas for calculating the surface area and volume of a triangular prism.
3. Practicing solving problems involving the surface area and volume of triangular prisms with different dimensions.

Additionally, it's helpful to visualize and draw different triangular prisms to gain a better understanding of their properties and how the formulas apply to real examples.

With a solid grasp of these concepts, you'll be well-prepared to tackle problems related to triangular prisms!