Length is a 1-dimensional concept. Length is a measure of the distance between two points. Length is operationalized by counting the number of identical sticks that can be connected in a line between the two points. The count is the measurement of length.

In the diagram below, the distance between the two points is 9 'sticks'.

Perimeter is the distance around a shape, where you return to the starting point. In other words, perimeter is the distance from a point back to itself.

The perimeter shown in this diagram is 17 'sticks'.

Try these:
What is the distance between point A and Point B?
What is the perimeter of the shape shown below?
Area is a 2-dimensional concept. Area is a measure of the amount of surface a shape has. Area is operationalized by counting the number of identical squares that cover the surface of a shape. The count is the measurement of area.
In the diagram shown on the right, the area of the shape is 12 'squares'.
Note that the perimeter of the shape is 16 'sticks'. You count the side length of a square to measure perimeter. You DO NOT count squares.
Try these:

What is the area and perimeter of each shape shown below?

Volume is a 3-dimensional concept. Volume is a measure of the amount of space in a 3-D object. Volume is operationalized by counting the number of identical cubes that fill the object. The count is the measurement of volume. In the diagram on the right, the volume of the object is 6 'cubes'.
Try these:

What is the volume of each 3-D object?