## Monday, January 23, 2012

### Perimeter

What is perimeter?

Perimeter is the ‘skin’.  It is the outside of a shape.  It doesn’t care about the inside. We can put a string on the outside of a shape and then straighten the string to find the perimeter. A real string can be held loosely or pulled very tight.  The 'mathematical string' below does not sag or stretch.  Move the slider (from left to right)to watch the string unwrap itself from the regular pentagon.  How long is the string?  How long is the outside of the pentagon?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Since perimeter doesn't care about what is inside we can rotate bits of the perimeter (as we did above) or we can slide bits of perimeter (the technical word is 'translate,' but not from Bahasa Malaysia to English or vice versa!). Sliding a bit of perimeter parallel to its original position can be very useful. Try the sliders below.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

You should have seen that the perimeter of an 'L-shape' is identical to the perimeter of the rectangle that could enclose or surround the L-shape.  Can you see that is a useful 'trick'?  Why?  Because we have a formula for the perimeter of a rectangle, P = 2 L + 2 W.  Some of you may prefer to add first and then multiply.  If so, P = 2(L + W).

When doing Mathematics, always be on the look-out for ways of changing the things that don't matter to clarify the things that do matter.