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A unit square is rotated 45 degree counterclockwise about one of its vertices, A. What is the green area?

 

 May 5, 2020
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A unit square is rotated 45 degrees counterclockwise about one of its vertices, A. What is the green area?

 

 

Draw a diagonal from  point A to the opposite corner. Now we have 2 isosceles green triangles.

 

The area of a larger triangle is    (1*1) / 2 = 0.5 u²

 

The length of a diagonal is          sqrt(2) = 1.414213562

 

The side of a small green triangle is         1.414213562 - 1 = 0.414213562

 

The area of a small triangle is                   ( 0.414213562 )² /2 = 0.085786437 u²

 

The green area is                               Agreen = 0.5 u² + 0.085786437 u² = 0.585786437 u²   indecision

 May 5, 2020
edited by Guest  May 5, 2020

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