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Diagonal Hint for a Rectangular Prism

Most rooms (in buildings and houses) can be considered to be rectangular prisms. Suppose we know the dimensions of such a room (length, width, height). How can we use these dimensions to calculate the distance from one corner of the room to its opposite corner? Interact with the applet below for a few minutes. (LARGE POINTS ARE MOVEABLE). Then, answer the questions that follow. To explore in GeoGebra Augmented Reality, see the directions below this applet.


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.


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. 2) Press the 3 horizontal bars (upper left corner). Select OPEN. 3) In the SEARCH TAB that appears, type NNUNEtR8. Note this string of characters can be found in the URL here. Be sure to either copy & paste this code or type it just the way you see it here. You should see a rectangular prism appear. 4) The LENGTH, WIDTH, and HEIGHT sliders control the dimensions of the prism. The ANIMATE slider does the animation.