Answer:
4 square units
Step-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.
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<h3>formula</h3>
Pick's theorem tells you the area is ...
A = i +b/2 -1
where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).
<h3>application</h3>
Using the counted values in the formula, we find the area to be ...
A = 0 +10/2 -1 = 4
The area of the polygon is 4 square units.
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<em>Additional comment</em>
There are several other ways to find the area. Here are a couple:
<u>decompose the figure</u>
A 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) = 5/2
The triangle has base 1 and height 3, so its area is ...
A = 1/2bh = 1/2(1)(3) = 3/2
Then the total area is 5/2 +3/2 = 8/2 = 4 square units.
<u>subtract empty space</u>
The 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
