Point A is at (4,1).
Point B is at (1,5).
Imagine drawing that blue triangle with a point at (1,1).
The distance of that bottom side would be (4-1) = 3.
The distance of the left side would be (5-1) = 4.
You can just could these distances on the graph or subtract the coordinates.
Now use the pyth. Theorem to find the hypotenuse, which is the length of one of the edges of the square.
3^2 + 4^2 = c^2
9+16 = 25 = c^2, so c = 5.
All sides of a square are the same.
AB = 5
BC = 5
CD = 5
DA = 5
Perimeter = 5+5+5+5 = 20 units
Area = 5x5 = 25 sq units.
See screenshot attached.
Have a good afternoon.