If the sides of a Triangle are divided in the ratios , , and , the Cevians form a central Triangle whose Area is

(1) 
where is the Area of the original Triangle. For
,

(2) 
For , 2, 3, ..., the areas are 0, 1/7, 4/13, 3/7, 16/31, 25/43, .... The Area of the Triangle formed by
connecting the division points on each side is

(3) 
Routh's theorem gives Ceva's Theorem and Menelaus' Theorem as special cases.
See also Ceva's Theorem, Cevian, Menelaus' Theorem
References
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 211212, 1969.
© 19969 Eric W. Weisstein
19990525