Find the area $\mathrm{K}$ of the triangle. \[ a=8, c=1, B=120^{\circ} \]

Step 1 ：We are given a triangle with side lengths a = 8, c = 1, and the angle B = 120 degrees between them. We are asked to find the area of the triangle.

Step 2 ：The formula to find the area of a triangle when two sides and the included angle are known is \(K = \frac{1}{2}ac\sin B\).

Step 3 ：Substituting the given values into the formula, we get \(K = \frac{1}{2} * 8 * 1 * \sin 120\).

Step 4 ：Calculating the above expression, we find that the area of the triangle is approximately 3.464101615137755.

Step 5 ：\(\boxed{3.464101615137755}\) is the final answer.