# Diagonal Hint for a Rectangular Prism

- Author:
- Tim Brzezinski

- Topic:
- 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.**## 1.

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.

## 2.

Same question as (1) above: Yet this time assume the dimensions of the box are 5 ft, 6 ft, and 8 ft.

## 3.

Describe, in your own words, how we can calculate the length of the diagonal of any rectangular prism.

## TO EXPLORE IN AUGMENTED REALITY:

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.