Geometry
1.7: Perimeter, Circumference, and Area
Name: _________________________________________________
Investigate: Perimeter and Area Date: ___________________________________________________
Essential Questions: How can you use a graphing calculator to find the smallest possible perimeter for a rectangle with a given area?
You can use formulas, P= 2 l
+ 2w and A = l
w, to find perimeter P and area A of a rentangle with length l and width w.
Step 1: Use the graph paper below to draw different rectangles, each with an area of 36 square units.
Use lengths of 2, 4, 6, 8, 10, 12, 14, 16, and 18 units.
Step 2: Using the graphing calculator Hit STAT  Edit. Enter lengths in List 1. Use the keystrokes below to calculate and enter the rectangle widths and perimeters in List 2 and List 3.
Keystrokes for entering widths in List 2:
Keystrokes for entering Perimeters
in List 3:

Step 3: Make a scatter plot using your graphing calculator, follow the keystrokes below- a.) Hit 2 nd STAT PLOT (y=)  Enter  Enter  click down so the cursor is blinking on L
2
 hit 2 nd
LIST (STAT)  click down to choose 3  Enter  ZOOM  click down so the cursor is on 9 
GRAPH. b.) Use the TRACE feature to see the coordinates of each point.
Step 4: Draw a sketch of the scatterplot you created.
Draw Conclusions:
1. In the scatter plot you made, what does the X-Axis represent?
2. What does the Y-Axis represent?
3. How can you use your scatter plot to determine which rectangle has the smallest perimeter?
4. What is the value of the smallest perimeter?
5. What do you notice about the shape of the rectangle with the smallest perimeter?