Math with Mr. J: Finding the Volume of a Triangular Prism

Introduction

• Volume Definition: The amount of space an object takes up.
• General Volume Formula for Prisms: Area of the base (B) times the height (H).
  • B: Area of the base.
  • H: Height of the prism.

Specifics for Triangular Prisms

• Triangular Bases: Use formula for area of a triangle.
  • Formula: Base (b) times height (h) divided by 2.
• Triangular Prism Volume Formula:
  • Volume = (Base of triangle * Height of triangle / 2) * Height of prism.

Example Calculations

Example 1

• Triangular Base:
  • Base = 5 cm
  • Height = 4 cm
• Height of Prism: 6 cm
• Volume Calculation:
  • Area of base = (5 * 4) / 2 = 10 cm²
  • Volume = 10 cm² * 6 cm = 60 cm³
• Conclusion: Volume is 60 cubic centimeters.

Example 2

• Triangular Base:
  • Base = 10 inches
  • Height = 7 inches
• Height of Prism: 3 inches
• Volume Calculation:
  • Area of base = (10 * 7) / 2 = 35 inches²
  • Volume = 35 inches² * 3 inches = 105 inches³
• Conclusion: Volume is 105 cubic inches.

Recap and Conclusion

• Process Recap: Calculate the area of the triangular base, then multiply by the height of the prism.
• Key Steps:
  • Identify base and height of the triangle.
  • Compute the area of the triangular base.
  • Multiply by the distance between the bases (height of the prism).

Closing

• Goal: Provide understanding of how to calculate the volume of a triangular prism.
• Thank you for watching!