When working on the TI-Nspire, many situations might arise that require you to investigate a geometric object numerically and algebraically. Take, for example, the situation in which you want to determine the maximum area enclosed by a rectangle with a fixed perimeter.

To analyze this situation, open a Geometry page and press **[MENU]**→View→Show Analytic Window. Press **[TAB]** until the word *axes* appears to change the size of the analytic window. See the first screen. Set your analytic window to have the same window settings as those shown in the second screen. Add a separate page with a Lists & Spreadsheet application. See the third screen.

You are now ready to construct a rectangle and obtain some measurements. Here are the steps to follow:

Press [MENU]→Shapes→Rectangle to access the Rectangle tool.

Move the cursor to place the upper-left corner of the rectangle and press

**[CLICK]**.Press

**[SHIFT]**, then move the cursor to place the upper-right corner of the rectangle and press**[CLICK]**. (Pressing the Shift key allows for movement in 15-degree increments.)Move the cursor to place the lower-right corner of the rectangle and press

**[CLICK]**.

Press [MENU]→Measurement→Length to open the Length tool.

To measure the perimeter of the rectangle, move the cursor to the rectangle until you see rectangle

**[TAB]**. Press**[CLICK]**to measure the perimeter of the rectangle. Move the measurement using the Touchpad keys and press**[CLICK]**to drop the measurement in place.Move the cursor to the side that represents the length of the rectangle until you see rectangle

**[TAB]**again. Press**[TAB]**to reveal side**[TAB]**. Press**[CLICK]**to measure the length of this side of the rectangle, rather than the perimeter of the rectangle. Move the measurement using the Touchpad keys and press**[CLICK]**to drop the length measurement in place.

Press [MENU]→Measurement→Area to access the Area tool.

Move the cursor to any side of the rectangle and press

**[CLICK]**to measure the area of the rectangle. Move the measurement using the Touchpad keys and press**[CLICK]**to drop the measurement in place.

Two of your measurements should be in centimeters (*cm*), the larger of which represents the perimeter. The area measurement is units of square centimeters (*cm*^{2}). Your diagram should resemble the first screen.

The next step is to lock the perimeter. This allows you to manipulate the rectangle while maintaining a fixed perimeter. To accomplish this task, move the cursor to the perimeter measurement and press **[CTRL][MENU]**→Attributes to open the Attributes control panel. Press

to highlight the Lock icon and then press

to lock the perimeter. See the second and third screens.

Recall that you want to analyze the relationship between the length of the rectangle and its area for a fixed perimeter. To explore this relationship, you must store these values as variables. Follow these steps:

Move your cursor to the length measurement from the previous Step 2 and press [CLICK] to highlight the measurement (as indicated by the gray box).

Press [VAR]→Store Var, type

*length*, and press [ENTER].This stores the length measurement as the variable

*length**.*A stored variable is always displayed in a bold font.

Move your cursor to the area measurement and press [CLICK] to highlight the measurement.

Another method of storing a variable is to right-click. Press [CTRL][MENU]→Store, type

*area*, and press [ENTER].