# A.4.4.3 Rules for Area and Perimeter

- Author:
- Katie Akesson

A square that has a side length of 9 cm has an area of 81 cm^{2}. The relationship between the side length and the area of the square is a function.
Complete the table below with the area for each given side length.
Then in the space below, write a rule for a function, A, that gives the area of the square in cm^{2} when the side length is s cm. Use function notation.
(you can use a *caret*, which is this symbol ^, to mean an exponent, i.e. x squared is x^2 or you can type it by holding down the "Alt" key, type 0178, and then let go of "Alt")

What does A(2) represent in this situation? What is its value?

A roll of paper that is 3 feet wide can be cut to any length. If we cut a length of 2.5 feet, what is the perimeter of the paper? Complete the table below with the perimeter for each given side length. Then in the space below, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l. Use function notation.

What does P(11) represent in this situation? What is its value?

How would you describe to a classmate who is absent today what each equation means? What would you say to help them make sense of these?

How do the rules help us find the value of f(10) or g(10)?

Is it possible to graph a function described this way? How?