Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 22

$$A=\sqrt{6479}$$

By Heron's Formula, we know: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ Where: $$s=\frac{a+b+c}{2}$$ Thus, we find: $$ s=\frac{12+20+30}{2}=31 \\ A=\sqrt{31\left(31-12\right)\left(31-20\right)\left(31-30\right)} \\ A=\sqrt{6479}$$