Four equilateral triangles are constructed on the sides of a square with side length 1, as shown below. The four outer vertices are then joined to form a large square. Find the area of the large square.
Let L be the side length of square.
By Law of Cosines,
\(L = \sqrt{1^2 + 1^2 - 2(1)(2)\cos 150^\circ} = \sqrt{2 + 2\sqrt 3}\)
Area of large square = \(L^2 = 2 + 2\sqrt 3\)
Hi, Max! What are you doing here? Can you, please, explain it?
Area = ( 1 + √3 )2 / 2
