What is the exact area (in square centimetres) of an equilateral triangle having side length 6 cm?

Introduction / Context:The area of an equilateral triangle with side a is a direct formula question, frequently tested for speed and accuracy. Remembering or deriving the formula quickly is key.

Given Data / Assumptions:

• Side length a = 6 cm.
• Use the standard equilateral triangle area formula.

Concept / Approach:The exact area is A = (√3/4) * a^2. This follows from splitting the triangle into two 30-60-90 right triangles and using the altitude a√3/2.

Step-by-Step Solution:

Verification / Alternative check:Altitude h = a√3/2 = 6√3/2 = 3√3. Then A = (1/2) * base * height = (1/2) * 6 * 3√3 = 9√3, consistent.

Why Other Options Are Wrong:

• 36√3: Multiplies by √3 without the 1/4 factor.
• 9 or 36: Misses the √3 factor entirely.

Common Pitfalls:Dropping the √3 factor or mis-squaring the side (6^2 = 36).

Final Answer:9√3