Geometry

Question Analysis:
This question involves working backwards from given surface area information to determine a missing dimension of an equilateral triangular prism.
The main focus is on understanding the relationship between perimeter, lateral area, and prism height.

Key Concept Explanation:
For any prism:
Lateral Surface Area (LSA) = Perimeter of base × Height
For equilateral triangle base: All three sides are equal (Perimeter = 3 × side length)

Step-by-Step Solution:
Given LSA = Perimeter × Height → 216 = P × 12 → P = 18
For equilateral triangle: Perimeter = 3 × side length
18 = 3 × side → side = 6 cm

Common Mistakes:
Confusing lateral area with total surface area
Using wrong formu...