设BA＝a﹙向量﹚.BC＝b.
BI＝tBE＝t﹙2a+b﹚/3＝BD+sDA＝b/2+s﹙a-b/2﹚＝sa+[﹙1-s﹚2]b 得到t＝3/4 s＝1/2
BG＝uBE＝u﹙2a+b﹚/3＝BC+vCF＝b+v﹙a/4-b﹚＝﹙v/4﹚a+﹙1-v﹚b 得到u＝1/3
BG∶GI∶IE＝4∶5∶3
BH＝BD+mDA＝b/2+m﹙a-b/2﹚＝BC+nCF＝﹙n/4﹚a+﹙1-n﹚b 得到m＝1/7
DH∶HI∶IA＝2∶5∶7
S⊿GHI＝﹙5/7﹚S⊿GDI＝﹙5/7﹚﹙5/9﹚S⊿BDI
＝﹙5/7﹚﹙5/9﹚﹙1/4﹚S⊿ABC＝25/252≈0.1