Area of an Equilateral Triangle (side = 8 cm): Find the area (in cm^2) of an equilateral triangle whose side length is 8 cm.

Introduction / Context:The area of an equilateral triangle can be computed directly from side length using a fixed constant multiplier. This avoids trigonometric detours and emphasizes formula recall and clean substitution with units carried consistently.

Given Data / Assumptions:

• Side a = 8 cm
• Area formula: A = (√3/4) * a^2
• All lengths in centimetres

Concept / Approach:Substitute a = 8 into A = (√3/4)a^2. Since a^2 = 64, the product streamlines neatly. Reporting the exact radical form (rather than decimals) keeps precision and matches typical aptitude answer formats.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 64 cm^2 is the square area, not the triangle's.
• 4√3 cm^2 corresponds to side 4 cm.
• 21.3 cm^2 is an inaccurate decimal; exact is 27.7…
• 32√3 cm^2 doubles the correct value.

Common Pitfalls:

• Using (1/2)ab with a wrong height; ensure equilateral height is (√3/2)a.

Final Answer:16√3 cm2.