The quadrilateral is a trapezoid and the area of the quadrilateral is 85.04 square units
<h3>How to determine the quadrilateral?</h3>The vertices are given as:
A:(-2, 3) B:(4, -6) C:(10, 2) D:(6, 8)
Next, we plot the vertices (see attachment)
From the attached graph, we can see that the quadrilateral is a trapezoid
<h3>How to determine the area?</h3>From the plot, we have the following features:
Height: AD
Parallel sides: CD and AB
Calculate the lengths using:
So, we have:
The area is then calculated as:
Area = 0.5 * (CD + AB) * AD
This gives
Area = 0.5 * (√52 + √117) * √89
Evaluate
Area = 85.04
Hence, the area of the quadrilateral is 85.04 square units
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