



A
square has four sides that are all the same length.



Like
this: 











Another
special thing about a square 


is that
all of the angles are the same size. 


They all
measure 90 degrees. 











If
something has four sides 


and they
are all the same length 


and four
angles inside 


and they
are all 90 degrees. 


IT'S A
SQUARE 





One other
thing about a square, 


is that
the sides across from each other 


are all
parallel. 





To find
the area of a square, 


just
multiply the length times the width. 





This is
pretty easy to do with squares 


because
the length and width are the same number. 











If you
draw a line from the top left corner of a square 


to the
bottom right corner of the square ... 











You get a
line called a diagonal. 


(It goes
diagonally across the square.) 


So for
once, one of these fancy math names names sense! 





This line
cuts the 90 degree angles 


at the
corners of the square exactly in half. 











This
diagonal is also part of a right triangle 


that is
hidden in the drawing. 











That
means, 


if we
know how long the sides of the square are ... 


we can
figure out the length of the diagonal! 











There is
nothing special about the two corners 


we used
to make the diagonal lines. 


We could
also use the other two corners 


to draw
the diagonal line. 











This one
also cuts the corners exactly in half. 











And makes
some right triangles inside the square. 











The sides
of the square are the same size 


as they
were a moment ago. 


That
means that this diagonal line will work out to be 


the same length as
the other one was. 











Where the
two diagonal lines cross in a square, 


two
special things happen. 


1) They
both cut each other exactly in half 


2) All
the angles at the cross are 90 degrees 


That
means we now have four right triangles 


hidden
in the square. 











These
little right triangles are all the same size as each other. 











If we
know how long the sides of the square are, 


we can
figure out the length of the sides of these little triangles. 





Example: 


Figure
out the length of the short triangle sides 


when the
length of each of the sides of the square is 5. 





The short
triangle sides are the same size as each other. 


Call each
one X. 











Some
people, OK mostly math people, 


don't
like to see roots on the bottom of a fraction (the denominator). 





We can
get the root out of there 


by
multiplying the answer by a special name for 1. 


This
name: 











So we
get: 











Math
people just love that last step (don't ask me why). 





copyright 2005 Bruce Kirkpatrick 
