Answer:
The area of the given Polygon is:
[tex]36\ unit^2[/tex]
Step-by-step explanation:
The polygon is in the shape of the trapezoid with two bases AB and CD and altitude as: AD
Now we know that the area of trapezoid is given by:
[tex]\text{Area}=\dfrac{1}{2}\times (\text{Sum of bases})\times \text{Altitude}[/tex]
i.e.
Here
[tex]\text{Area}=\dfrac{1}{2}\times (AB+CD)\times AD[/tex]
Now, we find the length of AB,CD and AD using distance formula.
A is located at (-2,5)
B at (3,5)
C at (5,-1)
D at (-2,-1)
[tex]AB=\sqrt{(-2-3)^2+(5-5)^2}\\\\i.e.\\\\AB=\sqrt{(-5)^2+0^2}\\\\i.e.\\\\AB=\sqrt{25}\\\\i.e.\\\\AB=5\ units[/tex]
[tex]CD=\sqrt{(5-(-2))^2+((-1)-(-1))^2}\\\\i.e.\\\\CD=\sqrt{7^2+0^2}\\\\i.e.\\\\CD=7\ units[/tex]
[tex]AD=\sqrt{(-2-(-2))^2+(5-(-1))^2}\\\\i.e.\\\\AD=\sqrt{0^2+6^2}\\\\i.e.\\\\AD=6\ units[/tex]
Hence, the area of Trapezoid is:
[tex]Area=\dfrac{1}{2}\times (5+7)\times 6\\\\i.e.\\\\Area=36\ unit^2[/tex]
