Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 29

$$A=\frac{3\sqrt{9077915}}{4}$$

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: $$s=\frac{81+67+71}{2}=\frac{219}{2} \\ A=\sqrt{\frac{219}{2}\left(\frac{219}{2}-81\right)\left(\frac{219}{2}-67\right)\left(\frac{219}{2}-71\right)} \\ A=\frac{3\sqrt{9077915}}{4}$$