What is the exact area (in square centimetres) of an equilateral triangle having side length 6 cm?
Aptitude
Area
Difficulty: Easy
Choose an option
-
A36√3
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B9
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C36
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D9√3
Answer
Correct Answer: 9√3
Explanation
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:
A = (√3/4) * a^2= (√3/4) * 36= 9√3 square centimetresVerification / 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