+4 An equilateral triangle is constructed on each side of a square with side length 2. The four outer vertices are then joined to form a large square. Find the side length of the large square.
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+2668 The side will be the length of the segment connecting the two vertices of the triangles.
This is a triangle with one angle of 120 degrees and 2 sides of 2.
By the Law of Cosines, the side of the square is \(\sqrt{2^2 + 2^2 - 2 \times 2 \times 2 \times \cos (150)} = {\color{brown}\boxed{\sqrt{8 + 4 \sqrt 3}}} \approx {3.864}\)
