Please answer these three questions.
Why is perimeter measured in units?
Why is area measured in square units?
Why is volume meassured in cube units?
Please give examples to clarify your explanations and they don't have to be "real-life" examples.
The perimeter of a 2 dimensional figure is derived by adding the lengths of the sides of the figure. For example, the perimeter of a square is the 4*s, where s is the length of the side. For a rectangle the perimeter is 2*(l + w) where l and w are the lengths of the sides of the rectangle. As the perimeter is found by just adding the lengths of the sides it is expressed in terms of units of length.
The area of a 2-dimensional or 3-dimensional figure is determined by multiplying the lengths of two sides. For example, in the case of a rectangle and a square the area is the product of the length of two sides. In the case of a triangle, the area is (1/2)*base*height. In every formula used to find the area of a figure, the area is the product of two lengths, this leads to the area being expressed in terms of square units.
To determine the volume of a 3-dimensional figure, we have to multiply the lengths of three sides of the figure. For example the volume of a cube is s*s*s where s is the length of the side, for a cuboid the volume is l*w*h where l, w and h are the lengths of the three sides of the cuboid. This makes the volume expressed in terms of cube units.