The ABC triangle is isosceles. angle B is 60 degrees. side of the AC – 8 cm, find the area of this triangle

The condition does not say whether the angle B is at the top or at the bottom. If at the top, then there are two corners at the base of 120 ° and each of them is 60 °. And accordingly, if the angle is B at the base, then the angle at the apex is 60 °. This triangle is equilateral. We find the area by the formula:
SABC = √3 / 4 * a² = √3 / 4 * 64 = 16√3 (cm²).
Answer: the area of the triangle ABC is 16√3 cm².