A square within a square...

Geometry Level 3

Let ABCD be a square. An equilateral triangle is placed on each side of the square, such that the base covers the whole side. Now join up the \({exposed}\) corners of the equilateral triangles (only join \({adjacent}\) corners) such that a larger square, PQRS, is formed. What is the value of \(\frac{area of PQRS}{area of ABCD}\)? ( give your answer to 2dp)

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