The smaller square in the diagram has side length 1. Equilateral triangles are constructed on its four sides, as shown. What is the area of the larger square?
I figured out that the biggest angle in the unknown triangle is 150 degrees since the small square is 90 degrees and the two equilateral triangle angles are 120 degrees
Diagram
http://imgur.com/download/AXf7hTm
+129840 This isn't as difficult as it seems.....the area of the larger square can be found by applying the Law of Cosines directly.to one of the non-equilateral triangles ........
Letting s be the side of the larger square....we have
s^2 = 1^2 + 1^2 - 2(1)(1)cos(150) = [2 + √3 ] ≈ 3.732 units^2
But...since s^2 is the area of the larger square.....this just kind of "falls out".......
Hope that helps.....
