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