The area of trapezoid is 46.95 square unit.
Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides.
The formula for the area of trapezoid is given by
[tex]Area = \frac{b_{1} +b_{2} }{2}h[/tex]
Where,
[tex]b_{1}[/tex] and [tex]b_{2}[/tex] is the base
And h is the height
According to the given question.
We have a trapezium ABCD.
In trapezium Sides AD and BC are parallel to each other.
And the length of sides
[tex]AD =b_{1} =\sqrt{(16-12)^{2} +(10-8)^{2} } =\sqrt{20}[/tex]
And,
[tex]BC =\sqrt{(14-6)^{2} +(16-12)^{2} } =\sqrt{80}[/tex]
And height
[tex]h = \sqrt{(16-9)^{2} +(14-14)^{2} } =\sqrt{49} =7[/tex]
Therefore, the area of the trapezoid is given by
[tex]Area =\frac{\sqrt{80} +\sqrt{20} }{2} (7)[/tex]
[tex]Area = \frac{13.41}{2} (7)[/tex]
[tex]Area = \frac{93.91}{2}[/tex]
[tex]Area = 46.95 square unit[/tex]
Hence, the area of trapezium is 46.95 square unit.
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