Lecture on Volume and Surface Area of a Triangular Prism

Introduction

Understanding the Shape: A triangular prism is essentially half of a rectangular prism.
Formula for Volume:
- Volume = 1/2 × Base Area × Height of the prism
- Base Area (triangle) = 1/2 × base × height
- Volume = 1/2 × (base of triangle) × (height of triangle) × (length/prism height)

Components:
- Surface Area = Base Area + Lateral Area
- Base Area = 2 × (1/2 × base × height) = base × height (for both triangles)
- Lateral Area = Perimeter of triangular base × length of the prism
Finding Perimeter:
- Perimeter = base + height + hypotenuse (Pythagorean theorem if necessary)
Final Formula for Surface Area:
- Surface Area = base × height + perimeter × length of the prism

Example 1:
- Given: Length = 6 in, Base = 3 in, Height = 4 in
- Volume Calculation: 1/2 × 3 × 4 × 6 = 36 cubic inches
- Hypotenuse Calculation: C = 5 in (using Pythagorean theorem)
- Surface Area Calculation: Perimeter = 12 in, Surface Area = 84 square inches
Example 2:
- Given: Length = 10 cm, Base = 5 cm, Height = 4 cm
- Volume Calculation: 1/2 × 5 × 4 × 10 = 100 cubic cm
Example 3:
- Given: Length = 15 units, Base = 6 units, Triangle sides = 6, 8, and 10
- Surface Area: Perimeter = 24 units, Surface Area = 408 square units
- Volume Calculation: Volume = 360 cubic units

Additional examples to find volume and surface area of various triangular prisms using given dimensions.

Understand and differentiate between base, height, and length of the prism.
Apply Pythagorean theorem for calculating missing dimensions in right triangles.
Recognize when to calculate only lateral area.
Ensure proper units: surface area in square units, volume in cubic units.

Mention of an algebra course available on Udemy for further learning on related mathematics topics.