Question
If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
- \(4\sqrt 6 \)
- \(6\sqrt 6 \)
- \(\sqrt 6 \)
- \(2\sqrt 6 \)
Option: 4
Solution:
Area of a regular hexagon = \(\frac{{3\sqrt 3 }}{2}{x^2}\) Area of an equilateral triangle = \(\frac{{\sqrt 3 }}{4}{\left( a \right)^2}\) ; where a = side of the triangle Since the area of the two figures are equal, we can equate them as folllows: \(\frac{{3\sqrt 3 }}{2}{x^2} = \frac{{\sqrt 3 }}{4}{\left( {12} \right)^2}\) On simplifying: \({x^2} = 24\;\) \(\therefore \;x = 2\sqrt 6 \)
Solution:
Area of a regular hexagon = \(\frac{{3\sqrt 3 }}{2}{x^2}\) Area of an equilateral triangle = \(\frac{{\sqrt 3 }}{4}{\left( a \right)^2}\) ; where a = side of the triangle Since the area of the two figures are equal, we can equate them as folllows: \(\frac{{3\sqrt 3 }}{2}{x^2} = \frac{{\sqrt 3 }}{4}{\left( {12} \right)^2}\) On simplifying: \({x^2} = 24\;\) \(\therefore \;x = 2\sqrt 6 \)
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