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Rhombus Area Calculator
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If you
took a steel box and jumped up and down on it,



it
might get to looking like this: 











All
of the sides would still be the same length, 


but
the angles wouldn't be 90 degrees any more. 


We
might have this: 











In
math, we call this shape a RHOMBUS. 


(WOW!
I wonder what planet they found that name on?) 





Anyway,
a rhombus is still like a square in some ways 



1)
All of the sides are still the same length. 



2)
Sides across from each other are still parallel. 





But
in one very important way, 


a
rhombus is very different from a square. 



1)
None of the angles are 90 degrees. 





The
sides of the rhombus that are across from each other are parallel. 


That
means we can play the old 


"Two
parallel lines and a line that crosses them" 


game
here too! 








Back
in the line game stuff, we had a rule that said 


that
if two parallel lines were crossed by another line, 


the
same side interior angles 


would
add up to 180 degrees, 





When
we have a rhombus, that bit of info really helps. 


It
tells us that ANY two angles that are next to each other 


will
add up to 180 degrees. 


Can
you see why? 





Just
roll the rhombus over onto the next side 


and
play the line game again. 











Example: 


Figure
out the measure of the angles in this rhombus ... 











OK,
in a rhombus two angles that are next to each other 


add
up to 180 degrees. 


So
that means we have: 











Now
just play the game with each of these angles 


and
the unknown angle next to it ... 


We
get: 








To
figure out the area of a rhombus 


we
need to know one more thing. 


We
need to know how far it is 


from
the top of the rhombus to the bottom. 











Here's
why ... 


If
we had a big knife, we could chop a corner off of the rhombus 


like
this: 











And
move the piece over like this: 











Now
we have a rectangle, 


and
rectangles are easy to deal with ... 





Example: 


Find
the area of this rhombus: 











Chop
it up and reassemble it ... 











Multiply
the length times the width 


to
get the area ... 








One
other thing you should know about a rhombus. 


A
rhombus has less area than a square 


that
has sides of the same length. 


(Hey,
if you squash something it will hold less stuff) 











The
diagonal lines in a rhombus work sort of like they do in a square: 



1)
They chop the corner angles exactly in half 



2)
They chop each other exactly in half 



3)
The angles we get where they cross are exactly 90 degrees 





They
are different from the diagonal lines in squares in one big way: 



1)
Rhombus diagonals are NOT the same length as each other. 











copyright 2008 Bruce Kirkpatrick 
