Area is concerned with the two dimensional space covered in the plane, on another hand if we talk about the boundary of the closed figure, then it is called the perimeter of the closed figure.
Another difference that is observed between the two is that the unit of measurement of area is Square units, but we find that the length of the side of the closed figure is in inches, feet, etc. So we come to the conclusion that if we have a plot and we want to fence the plot, then we are concerned with the boundary of the closed figure, it means here we are concerned with the perimeter. But on another side if we have to make the flouring of the land, then we are talking about the area covered by the land, it indicates the area of the plot.
In a triangle the perimeter will be the sum of the three sides of the triangle and the Area of Triangle = (base *height) / 2.
Now we talk about the area and perimeter of the square. A square is the closed figure, which says that the sides of the square are equal. Let us say that the side of the square is x, then Area of the square = side * side.
So Area = x * x. But when we want to find the area of the square = sum of sides = 4 * x square units.