The line y= 1/2 crosses the curve y= sin x when sin x= 1/2 which is at

,

,

and

. Also, perhaps by looking at a graph, you should be able to see that some of those areas are exactly the same and that the total area is 4 times the area from x= 0 to

plus 2 times the area from

to

. Those two have to be done separately because between x= 0 and

1/2 is lower than sin x and between

and

, 1/2 is higher than sin x.

Now, since you put this in "geometry" rather than "calculus", what

**do** you know how to do? If you have learned how to "integrate" then you should know this area is

.

If you do not know how to integrate then I don't think it will be possible for you to do this problem.