Answer:
14 square units
Explanation:
You want to use Pick's theorem to find the area of the figure shown.
Pick's theorem
The area of a simple polygon can be found using the formula ...
A = i +b/2 -1
where i is the number of interior points, b is the number of boundary points.
We can divide the figure into three triangles and sum their areas.
Left triangle
The left triangle has 4 interior points and 12 boundary points. Its area is ...
A1 = 4 +12/2 -1 = 9 . . . . square units
Center triangle
The center triangle has 1 interior point and 8 boundary points. Its area is ...
A2 = 1 +8/2 -1 = 4 . . . . square units
Right triangle
The right triangle has 0 interior points and 4 boundary points. Its area is ...
A3 = 0 +4/2 -1 = 1 . . . . square unit
Total
The total shaded area is ...
A = A1 +A2 +A3 = 9 + 4 + 1 = 14 . . . . square units
The area of the shape is 14 square units.
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Additional comment
Here, we have treated the figure as 3 separate triangles. One can consider the figure as having one boundary containing 24 points (2 points are counted twice). Then the "-1" in the formula needs to be adjusted to "-3" to account for the fact that there are 3 separate enclosed areas:
A = 5 +24/2 -3 = 5 +12 -3 = 14 . . . . square units
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