Question

If ABC is equilateral triangle such that bd/bc=1/3 and ce/ca=1/3, af/ab=1/3. Find the ratio of area of the shaded region to area of abc

Answer 1

The question ask to calculate or to find the ration of the shaded region to area of ABC if ABC is equilateral triangle. Based on my calculation and further formulation, I came up with an answer of 1/7. I hope you are satisfied with my answer 

Answer 2

This is a well known math problem also called the Feynman's triangle. If the ABC is equilateral triangle, such that the bd/bc=1/3 and ce/ca=1/3, af/ab=1/3. Then the ratio of the area of the shaded region to area of abc is 60.

This is the work to the problem;
BE2=CE2+CB2−2.CE.CBcos(60) BE2=12+32−2.1.312 BE=7√ (1)