The Area of the Pedal Triangle of the Centroid
Connect the feet of the perpendiculars from the centroid of the triangle ABC to its sides to form the pedal triangle of the centroid. Let the area of be and the area of ABC be . Then .
See Problem 5 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 71.