Area of an equilateral triangle — Aptitude Question
Area of an equilateral triangle: What is the area of an equilateral triangle of side 12 cm? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the area of an equilateral triangle of side 12 cm?
Options
- 36√3 cm²
- 48√3 cm²
- 144√3 cm²
- 72 cm²
Show the answer and the worked solution
Correct answer: A. 36√3 cm²
Worked solution
- Area = (√3/4) × 12² = (√3/4) × 144 = 36√3 cm² (about 62.28 cm²).
Answer: 36√3 cm².
The idea
Learn (√3/4)a² for the area and (√3/2)a for the height. Both come up constantly in geometry questions.
Shortcut. The height is half the side times √3, i.e. 6√3, so the area is ½ × 12 × 6√3 = 36√3.
Common trap. 72 cm² — using ½ × base × side, as if the 12 cm side were the height; the height is only 6√3 ≈ 10.4 cm.