Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 28

$$A=\frac{15\sqrt{2627}}{4}$$

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: $$s=\frac{31+23+17}{2}=\frac{71}{2} \\ A=\sqrt{\frac{71}{2}\left(\frac{71}{2}-31\right)\left(\frac{71}{2}-23\right)\left(\frac{71}{2}-17\right)}\\ A=\frac{15\sqrt{2627}}{4}$$