Answer:
Part 1) The polygon is a square
Part 2) The perimeter is equal to 
Part 3) The area is equal to 
Step-by-step explanation:
we have

Plot the points
see the attached figure
we know that
the formula to calculate the distance between two points is equal to

Find the distance AB

substitute in the formula




Find the distance BC

substitute in the formula




Find the distance CD

substitute in the formula




Find the distance AD

substitute in the formula



we have that
AB=BC=CD=AD
Find the distance BD (diagonal)

substitute in the formula


<em>Verify if the polygon is a square</em>
If the triangle BDA is a right triangle, then the polygon is a square
Applying the Pythagoras theorem

substitute

-----> is true
so
The triangle BDA is a right triangle
therefore
The polygon is a square
<em>Find the Area of the polygon</em>
The area of a square is equal to

we have


<em>Find the perimeter of the polygon</em>
The perimeter of a square is equal to

we have

