Puzzle 103 - solution

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Let us say the side of equilateral triangle is x. 
Then its perimeter is 3x.

If the side of hexagon is y, its perimeter is 6y.

3x=6y  ---------since perimeters are same
y = 1/2x

Area of triangle is 2

2 = (√3/4)x²

Area of hexagon= (3√3 y2)/2 
Replacing y with x/2, we get
Area of hexagon =  (3√3 (x/2)2)/2 = (3√3 x²/4)/2 = 3/2 *  (√3 x²/4) = 3/2 * 2 = 3 units

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