In fact, it is the easiest to put the numbers together. The benefits of filling in the blanks

Solution:

Δ ABC is equilateral, g is the midpoint of Δ ABC, connecting AG/BG/CG, and AG=BG=CG.

Let AB=a, AG = BG = CG = √ 3/3 AD = AE = 2/3 BD = CE =1/3.

To make △BDM∽△CEM.

Known ∠DBC=∠BCE=60? There is DB/BM=CM/CE.

BM+CM=BC=a, let BM=x, CM =1-X.

Enumerable formula:1/3: x = (1-x):1/3.

X= 1/2+√5/6 or x= 1/2-√5/6.

S△BDM= 1/2×BD×BM×sin60？

S△CEM= 1/2×CE×CM×sin60？

S△BDM=√3/24+√ 15/72 or √3/24-√ 15/72.

S△CEM=√3/24-√ 15/72 or √3/24+√ 15/72.