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# Geometry question help quickly!

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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.

Aug 31, 2022

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You should always upload the picture. If you don't know how, then learn from the instructions on this site. See the answer and the uploaded picture here:

https://web2.0calc.com/questions/find-the-area-of-the-larger-square

Aug 31, 2022
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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 $$\sqrt{2^2 + 2^2 - 2 \times 2 \times 2 \times \cos (150)} = {\color{brown}\boxed{\sqrt{8 + 4 \sqrt 3}}} \approx {3.864}$$

Aug 31, 2022
edited by BuilderBoi  Aug 31, 2022