Perimeter and Area:

Combining Linear and Quadratic Functions

Objectives:

Given the length and width of a rectangle, find the perimeter of that rectangle.

Given the length and width of a rectangle, find the area of that rectangle.

Use data and Excel to graph functions

Analyze the graphs of linear and quadratic functions

Now that you have studied both linear and quadratic functions, you can determine real-world data that behaves as linear and quadratic functions.

 

Let's review the formulas for finding perimeter and area:

Perimeter = 2L +2W

Area = L*W

I. Using the given lengths and widths, find the perimeters and areas of the following rectangles.

Length  Width  Perimeter  Area
 1  4    
 2  6    
 3  8    
 4  10    
 5  12    
 6  14    
 7  16    
 8  18    
 9  20    
 10  22    
 11  24    
 12  26    
 13  28    
 14  30    
 15  32    
 16  34    
 17  36    
 18  38    
 19  40    
 20  42    

II. Use Excel to plot the data. Plot perimeter and are on the same set of axes and compare the graphs.

 

III. Analyzing the data/ Comparing Graphs

A. As the length increases, the perimeter

B. As the length increases, the area

C. Is Perimeter Linear or Quadratic?

D. Is Area Linear or Quadratic?

E. Explain why the graphs display the data in this manner?

Click here to see graphs

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