8/3/2019 Area and Volume of ALL Polygons
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Solving for the Area and Volume of Regular and Irregular
Polygons
There are preset formulas to calculate the area of each regular
polygon. The current methods present
the student with a multitude of formulas
to memorize. What if there were a
method to find the area and hence the
volume of any polygon regular or
irregular?Herons formulais suggested
as a one method does them all. Notice
that any polygon can be sectioned into
triangular shapes(Graphic 1).
For this specific example the point A
(Graphic 2) is used as a
reference point to section the irregular
octagon into six triangles. Since Herons formula makes use of
the length of
each side of a triangle, we will use thedistance formulato find
the length of
each.
It is worth noting that the
distance formula is based on
the right triangle and as such the Pythagorean Theorem.
There is the need, then, to superimpose a point to do
this ( . The length of the segment
measured in centimeters, is the hypotenuse
of the right triangle A(Graphic 3).
Therefore the segment
length
. Continuing on, we can find the
perimeter of the triangle
(Graphic 2). In order to use Herons formula we need to find
(thesemi perimeter) where
Graphic 1
Graphic 3
Graphic 2
http://en.wikipedia.org/wiki/Heron's_formulahttp://en.wikipedia.org/wiki/Heron's_formulahttp://en.wikipedia.org/wiki/Heron's_formulahttp://www.mathsisfun.com/algebra/distance-2-points.htmlhttp://www.mathsisfun.com/algebra/distance-2-points.htmlhttp://www.mathsisfun.com/algebra/distance-2-points.htmlhttp://www.mathsisfun.com/algebra/distance-2-points.htmlhttp://en.wikipedia.org/wiki/Heron's_formula
