Overview
The video explains how to find the surface area of a triangular prism by calculating the area of each face and adding them together.
Surface Area of a Triangular Prism
- Surface area is the total area of the outside layer of a 3D figure.
- A triangular prism has five faces: 2 triangular bases and 3 rectangular lateral faces.
- Strategy: find areas of all five faces, then sum them to get total surface area.
- Nets help visualize faces by unfolding the 3D prism into 2 triangles and 3 rectangles.
Formulas and Setup
- Triangle area formula: A = 1/2 × base × height.
- Rectangle area formula: A = length × width (or base × height).
- Surface area setup: SA = 2 × (area of base) + area of rectangle + area of rectangle + area of rectangle.
Example Problem Details
- Triangular bases are congruent; compute one and multiply by two.
- Given measures: base of triangle = 6 in, triangle height = 4 in, prism length = 7 in.
- Rectangles correspond to the three sides of the triangle extended along prism length.
Example Calculations Table
| Face | Dimensions | Area Calculation | Area (square inches) |
|---|
| Triangle (one base) | base = 6 in, height = 4 in | 1/2 × 6 × 4 | 12 |
| Both triangles | two congruent bases | 2 × 12 | 24 |
| Bottom rectangle | 7 in by 6 in | 7 × 6 | 42 |
| Right rectangle | 7 in by 5 in | 7 × 5 | 35 |
| Left rectangle | same as right | 7 × 5 | 35 |
| Total SA | sum of all faces | 24 + 42 + 35 + 35 | 136 |
Worked Example Steps
- Find triangle area: 1/2 × 6 × 4 = 12 square inches.
- Multiply by two for both bases: 2 × 12 = 24 square inches.
- Bottom rectangle: 7 × 6 = 42 square inches.
- Right rectangle: 7 × 5 = 35 square inches.
- Left rectangle: same as right = 35 square inches.
- Add: 24 + 42 + 35 + 35 = 136 square inches total.
Key Terms & Definitions
- Surface area (SA): Sum of the areas of all faces of a 3D figure.
- Prism: A solid with two congruent, parallel bases and rectangular lateral faces.
- Net: A 2D layout of a 3D figure’s faces unfolded flat.
- Congruent bases: Bases that are the exact same size and shape.
Action Items / Next Steps
- Practice multiple problems to improve speed and accuracy.
- Use a net to visualize and verify face dimensions before calculating.
- Organize work: compute base area, then each rectangle, then sum.