Analysis: According to the three-in-one nature of isosceles triangle, auxiliary lines can be added: point A is AD⊥BC, and point B is D. Only the long problem of BC and AD can be solved!

Solution: Take point A as AD⊥BC, and cross BC at point D.

AB = AC，∠BAC= 120

∴∠ b = 30 (the sum of the three internal angles of a triangle is 180).

∴ ad = (1/2) * ab = (1/2) * 4 = 2 (in a right triangle, the opposite side of 30 is equal to half of the hypotenuse).

According to Pythagorean theorem, BD=2√3 can be obtained.

∴BC=4√3 (isosceles triangle connected by three lines)

∴S△ABC=( 1/2)*4√3*2=4√3cm？ (triangle area formula)

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