Overview
This lecture covers the key formulas for prisms, including volume, lateral area, and total area, with examples of each calculation.
Volume of a Prism
- The volume (V) of a prism = area of the base (B) × perpendicular height (h).
- Multiplication order does not matter due to the commutative property.
- Example 1: Rectangular prism with base 5 × 4 and height 8 → V = 5 × 4 × 8 = 160 units³.
- Example 2: Triangular prism with right triangle base (½ × 3 × 4) and height 4 → V = 6 × 4 = 24 units³.
- Volume is always measured in cubic units.
Lateral Area of a Prism
- The lateral area (LA) = perimeter of the base (P) × height (h).
- Lateral area only includes the sides, not the top or bottom bases.
- Example: Prism with perimeter 18 and height 7 → LA = 18 × 7 = 126 units² (area units are always squared).
Total Area of a Prism
- Total area (TA) = lateral area + 2 × area of the base.
- Calculate the perimeter of the base, multiply by height for lateral area, then add the area of both bases.
- Example with hexagonal base: Perimeter = 3 × 6 = 18; height = 5; base area = 3 × 4 = 12.
- TA = (18 × 5) + 2 × 12 = 90 + 24 = 114 units².
Key Terms & Definitions
- Prism — A 3D shape with two parallel, congruent bases connected by rectangular faces.
- Volume — The amount of space inside a 3D object, measured in cubic units.
- Lateral Area — The surface area of all the sides (lateral faces) except the bases.
- Total Area — The sum of the lateral area and the areas of both bases.
- Perimeter — The total length around the base shape.
Action Items / Next Steps
- Review notes and practice problems with prisms.
- Prepare for the next lesson on right circular cylinders.