Surface Area of a Triangular Prism

Definition: Surface area (SA) measures the area that covers the surface of a prism.
Formula: [ SA = 2B + PH ]
- 2B: Represents the area of the two bases.
- P: Perimeter of the base.
- H: Height or distance between the two bases.

Identify the two bases of the prism:
- Both are congruent triangles.
Calculate the area of one triangular base:
- The formula for triangle area: [ Area = \frac{1}{2} \times base \times height ]
- For a right triangle:
  - Given base = 8 inches, height = 6 inches
- Calculation: [ 8 \times 6 = 48, \quad \frac{48}{2} = 24 \text{ inches}^2 ]
- Area of one triangle = 24 inches².
Areas of both bases:
- Since there are two bases: [ 2 \times 24 = 48 \text{ inches}^2 ]
Find base perimeter (P):
- Sum of all sides of the triangle.
- Known sides: 6 and 8 inches.
- Use the Pythagorean theorem to find the hypotenuse:
  - [ C^2 = A^2 + B^2 ]
  - Given sides: 8 and 6 inches: [ 8^2 + 6^2 = 64 + 36 = 100 ]
  - Thus, [ C = \sqrt{100} = 10 \text{ inches} ]
- Total perimeter of the triangular base: [ 6 + 8 + 10 = 24 \text{ inches} ]
Calculate Lateral Surface Area (LSA):
- Height (H) = distance between bases = 5 inches.
- Lateral Area: [ LSA = P \times H = 24 \times 5 = 120 \text{ inches}^2 ]
Final Calculation:
- Total Surface Area: [ SA = 2B + LSA = 48 + 120 = 168 \text{ inches}^2 ]