WOLFRAM|DEMONSTRATIONS PROJECT

The Area of the Pedal Triangle of the Centroid

​
S
≈
85.87
AB
≈
17.37
BC
≈
14.20
AC
≈
12.22
s
≈
20.22
4
3
S
(
2
AB
+
2
BC
+
2
AC
)
/
(
9
2
AB
×
2
BC
×
2
AC
)
≈
20.22
Connect the feet of the perpendiculars from the centroid of the triangle ABC to its sides to form the pedal triangle
P
of the centroid. Let the area of
P
be
s
and the area of ABC be
S
. Then
s=4
3
S
(
2
AB
+
2
BC
+
2
AC
)/(9
2
AB
×
2
BC
×
2
AC
)
.