Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 21

$$A=10\sqrt{65}$$

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: $$s=\frac{23+15+12}{2}=25 \\ A=\sqrt{25\left(25-23\right)\left(25-15\right)\left(25-12\right)} \\ A=10\sqrt{65}$$