Most rooms (in buildings and houses) can be considered to be rectangular prisms. [br][br]Suppose we know the dimensions of such a room (length, width, height). [br][br]How can we use these dimensions to calculate the distance from one corner of the room to its opposite corner? [br][br]Interact with the applet below for a few minutes. [b](LARGE POINTS ARE MOVEABLE).[/b] Then, answer the questions that follow. [br][color=#1e84cc][b][br]To explore in GeoGebra Augmented Reality, see the directions below this applet. [/b][/color]
Suppose the dimensions of the box above are 3 ft, 4ft, and 12 ft. Determine the length of the diagonal (segment that connects one corner to its opposite corner) of this prism.
Same question as (1) above: Yet this time assume the dimensions of the box are 5 ft, 6 ft, and 8 ft.
[math]\sqrt{125}=5\sqrt{5}[/math] ft
Describe, in your own words, how we can calculate the length of the diagonal of any rectangular prism.
1) Open GeoGebra 3D app on your device. [br]2) Press the 3 horizontal bars (upper left corner). Select OPEN. [br][br]3) In the SEARCH TAB that appears, type [b]NNUNEtR8[/b]. [br] Note this string of characters can be found in the URL here. [br] Be sure to either copy & paste this code or type it just the way you see it here. [br] You should see a rectangular prism appear. [br][br]4) The [b]LENGTH[/b], [b]WIDTH[/b], and [b]HEIGHT[/b] sliders control the dimensions of the prism. [br] The [b]ANIMATE[/b] slider does the animation.