View
224
Download
0
Category
Preview:
Citation preview
A Proof of Heron’s Formula
Let I be the center of the incircle of ∆ABC. Let a = y + z, b = x + z, and c = x + y be the
lengths of the sides opposite A, B, C respectively, and let s = x + y + z be the semiperimeter
of the triangle. Clearly so . Now notice that:
Therefore
so
Thus the area of ∆ABC is
which is Heron’s formula.
--Submitted by Miles Dillon Edwards
Lassiter High School, Marietta, GA 30066
December 2007
I
u
i
B
A
C
y
v r
z
z
y
x x
r r
w
Recommended