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