Area of an Equilateral Triangle (side = 8 cm): Find the area (in cm^2) of an equilateral triangle whose side length is 8 cm.
Aptitude
Area
Difficulty: Easy
Choose an option
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A64 cm2
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B16√3 cm2
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C21.3 cm2
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D4√3 cm2
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E32√3 cm2
Answer
Correct Answer: 16√3 cm2
Explanation
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:
Compute a^2: 8^2 = 64.Apply formula: A = (√3/4) * 64 = 16√3 cm^2.Approximate (optional): √3 ≈ 1.732 ⇒ A ≈ 27.712 cm^2.Verification / Alternative check:
Using height h = (√3/2)a = 4√3 ⇒ A = (1/2)*base*height = (1/2)*8*(4√3) = 16√3 cm^2.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.