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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.

 

 Jul 21, 2020
 #1
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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 = \(L^2 = 2 + 2\sqrt 3\)

 Jul 22, 2020
 #3
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Hi, Max! What are you doing here? Can you, please, explain it?

Guest Jul 22, 2020
 #2
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Area = ( 1 + 3 )2 / 2    laugh

 Jul 22, 2020

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