Stained Glass WindowsFinding
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: Windows: 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.
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