Area of the polygon is 37 square unit.
Area of the rectangle can be estimated by the product of the length and breadth of the rectangle.
Area of the rectangle = A=l*b
where l is length and b is breadth.
The distance between two points can be calculated by using the following formula:
d=√(y₂-y₁)²+(x₂-x₁)²
where (x₁,y₁),(x₂,y₂) is the coordinate of the points.
Here Polygon ABCD is a rectangle.
The coordinate of the vertices will be: A(-3,3), B(3,4), C(4,-2), D(-2,-3)
The area of the rectangle is equal to =A= AB*AD
Step-1: Find the length of AB
Where A(-3,3), B(3,4)
substituting the above point in the distance formula,
AB=√(4-3)²+(3-(-3))²
=√1²+6²
=√36+1
⇒AB=√37 unit
Step-2: Find the length of AB
Where A(-3,3), D(-2,-3)
substituting the above point in the distance formula,
AD=√(-3-3)²+(-2-(-3))²
=√(-6)²+1²
=√36+1
⇒AD=√37 unit
Step-3: to find the area of the rectangle,
Area of the polygon i.e. rectangle A =AB*AD
Where we have AB=√37 unit
and AD =√37 unit
Area =AB*AD
=√37*√37
=37 square unit
Therefore area of the polygon is 37 square unit.
Learn more about the area of rectangle
here: https://brainly.com/question/12794822
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