HERON'S FORMULA
See Also: Problem Solving with Heron's
Formula
Introduction
Heron's formula for the area of a triangle with sides of length
a, b, c is
where
Problem:
Develop a proof of Heron's Formula for the area of a triangle.
An Algebraic Proof
This demonstration of Heron's formula is straightforward and elementary.
Working through it with students can provide fruitful ideas of
strategy, symmetry, planning, and observation. We now switch to
consider some problems and investigations for which Heron's formula
is useful.
A Trigonometric Shortcut
In the algebraic proof, a value p was computed in terms of
a, b, and c. Consider the Law of Cosines and examine p as the
cosine of the angle between a and c.
A Trigonometric Proof
-- Considered by some mathematics people to be a "more elegant
approach." What do you think?
A Geometric Proof
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