Problem 2

 

ABCD is a two-by-two square.  E is the midpoint of AD.  Find the area of CDEF.

 

[Problem submitted by Juergen Pahl, LACC Professor of Mathematics.]

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Solution for Problem 2:

 

 and , therefore the area of triangle ABE is 1 and

 

 

 and ,

 

which means that ABE and BCF are similar triangles. 

 

Therefore 

 

 

Area of triangle BCF is then

 

Area of CDEF