Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 24

$$A=\frac{9\sqrt{143}}{4}$$

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: $$s=\frac{12+7+8}{2}=\frac{27}{2} \\ A=\sqrt{\frac{27}{2}\left(\frac{27}{2}-12\right)\left(\frac{27}{2}-7\right)\left(\frac{27}{2}-8\right)} \\ A=\frac{9\sqrt{143}}{4}$$