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EEJ MAIN Aptitude QUESTION #10967
Question 1
A regular hexagon is divided into 6 equilateral triangles. If the hexagon has an area of \(54\sqrt{3}\ \text{cm}^2\, what is the side length of the hexagon?
  • 6 cm✔️
  • 3 cm
  • 9 cm
  • 4 cm
Correct Answer Explanation

Area of regular hexagon with side \(s\: \(A = \dfrac{3\sqrt{3}}{2}s^2\

Setting equal: \(\dfrac{3\sqrt{3}}{2}s^2 = 54\sqrt{3}\

\(s^2 = \dfrac{54\sqrt{3} \times 2}{3\sqrt{3}} = \dfrac{108}{3} = 36\

\(s = 6\ \text{cm}\

Verification: \(\dfrac{3\sqrt{3}}{2} \times 36 = 54\sqrt{3}\ ✓