Stained Glass Windows

Finding the number of squares in a rectangular grid is easy, when you know the length and width. However, many floors are tiled ‘on the diagonal’, instead. How do you find the number of tiles needed?

Old or stained glass windows are often rectangular in shape, but are composed of many smaller ‘rhombi’ (diamonds), which are ‘tiled’ on the diagonal, too.

 The Problems:



Find the number of diamonds in the windows shown above, and deduce a quick way to do this, using only the original width and height of the ‘frame’.


A kitchen floor is tiled ‘on the diagonal’, with squares of diagonal width 18 cm.

The floor area measures 369 cm by 270 cm, and the tiles cost £1 each, fitted.


How much will this flooring cost altogether?


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Last modified: June 18, 2007