SOLUTION: The diagram below shows a square whose side is 1 and also two arcs with centres at points A and D. What is the area of the shaded surface? Diagram link: http://i66.tinypic.com

Algebra ->  Surface-area -> SOLUTION: The diagram below shows a square whose side is 1 and also two arcs with centres at points A and D. What is the area of the shaded surface? Diagram link: http://i66.tinypic.com      Log On


   

Question 1138494: The diagram below shows a square whose side is 1 and also two arcs with centres at points A and D. What is the area of the shaded surface?
Diagram link: http://i66.tinypic.com/2rr6ngp.jpg
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if side of square is 1, diagonal CB=sqrt%282%29
diagonal CB divides square in two equal parts, as shaded surface as well
the area of the arc with center at point A is:
A%5B1%5D=pi%2Ar%5E2%2890%2F360%29
A%5B1%5D=pi%2A%28sqrt%282%29%29%5E2%281%2F4%29
A%5B1%5D=pi%2A2%281%2F4%29
A%5B1%5D=pi%2F2

1%2F2%29 area of the square equal to
=>A%5B2%5D=%281%2F2%29%281%2A1%29=1%2F2
the area of the arc minus 1%2F2%29 area of the square will be1%2F2 of the shaded surface:
to get the shaded surface, multiply by 2
2%28A%5B1%5D-A%5B2%5D%29=2%28+pi%2F2-1%2F2%29=pi-1 -> approximately 2.14