The area of the polygon is approximately 24.497 square units.
How to determine the area of a polygon
In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:
JK = √[[4 - (- 3)]² + (4 - 4)²]
JK = 7
KL = √[(3 - 4)² + (- 3 - 4)²]
KL = √[(- 1)² + (- 7)²]
KL = 5√2
JL = √[[3 - (- 3)]² + (- 3 - 4)²]
JL = √85
Second, calculate the area of the triangle:
s = (JK + KL + JL) / 2
s = (7 + 5√2 + √85) / 2
s ≈ 11.645
A = √[s · (s - JK) · (s - KL) · (s - JL)]
A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]
A ≈ 24.497
The area of the polygon is approximately 24.497 square units.
To learn more on Heron's formula: https://brainly.com/question/20934807
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