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Question 46
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
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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