Math (Geometry)
posted by Robert .
"Target Games: Darts are thrown at each of the boards shown below. A dart hits the board at a random point. Judging by appearances, find the probability that it will land in the shaded region." This figure is a diamond (the diamond is not shaded) and it has half a circle attached to each side. (Shaded part) How can I do this problem without any numbers???

You can't do a probability problem without using numbers. They may be asking you to compare the shaded area with the total area, but the probability of hitting the shaded area also depends upon the distribution of where the darts hit. They are presumably not distributed uniformly all over the dart board.
Another confusing aspect of your question is that it starts out talking about "each of the boards shown below", but you only describe one of them. 
I only describe one because that is the one I am having trouble with, the others were simple since it would show a figure composed of 5 triangles and only 2 would be shaded. (2/5)

The ratio of semicircular areas to the total of semicircles plus the "diamond" area depends upon the shape of the diamond, which I assume to be a rhombus. Lacking the figure, we need a more complete description of the geometry to be able to help you.

well, sry. that's impossible to do.

the figure at right is a sguere. find an xepression for the area of the shaded region . write yuor answer in standard form.