Find the area of the shaded polygons:

Answer:   4 square unitsStep-by-step explanation:The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.__formulaPick's theorem tells you the area is ...   A = i +b/2 -1where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).applicationUsing the counted values in the formula, we find the area to be ...   A = 0 +10/2 -1 = 4The area of the polygon is 4 square units._____Additional commentThere are several other ways to find the area. Here are a couple:decompose the figureA horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...   A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2The triangle has base 1 and height 3, so its area is ...   A = 1/2bh = 1/2(1)(3) = 3/2Then the total area is 5/2 +3/2 = 8/2 = 4 square units.subtract empty spaceThe figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...   A = s² -1/2bh -1/2bh   A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units