Question 1197252
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Plot the given points and form a quadrilateral by joining up adjacent vertices
Eg: (5,2) connects to (4,3)


After doing that, mark lattice points on the boundary and lattice points inside the polygon.
A lattice point has both coordinates as integer values. It's where the dashed grid lines intersect.
<img src = "https://i.imgur.com/qzlE9Cl.png">
Each point marked has integer coordinates x,y
Red points are on the boundaries
Blue points are interior


b = number of boundary lattice points = number of red points = 8
i = number of interior lattice points = number of blue points = 15


Use Pick's Theorem
<a href = "https://mathworld.wolfram.com/PicksTheorem.html">https://mathworld.wolfram.com/PicksTheorem.html</a>
<a href = "https://en.wikipedia.org/wiki/Pick%27s_theorem">https://en.wikipedia.org/wiki/Pick%27s_theorem</a>
to get this
A = area of the polygon
A = i + 0.5*b - 1
A = 15 + 0.5*8 - 1
A = 15 + 4 - 1
A = 19 - 1
A = 18


Answer: The area of the quadrilateral is 18 square units


Keep in mind that Pick's Theorem only applies if all vertex or corner points are lattice points.


Another approach you could use is the shoelace formula (see this <a href="https://www.algebra.com/algebra/homework/Parallelograms/Parallelograms.faq.question.1204418.html">example problem</a> )
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