How would I find the area of the shaded polygon?

http://tinypic.com/view.php?pic=2r3xjzr&s=6

Question

How would I find the area of the shaded polygon?

http://tinypic.com/view.php?pic=2r3xjzr&s=6

directrix · Answer

Get the area of the outer square (in red). It has dimensions 5 by 5 so its area is 25.
Next, find the areas of each of the 4 unshaded right triangles inside the square. Subtract those from 25 and the area that is left will be the area of the shaded region.

To help you get started on the triangle areas, look at the lower left right triangle. It has legs of length 4 and 3. Its area is 1/2 (4*3) = 6. Do the same with the other 3 triangles.