Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - Guided Practice for Example 4 - Page 891: 4

$$A=4\sqrt{21}$$

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: $$s=\frac{5+8+11}{2}=12 \\ A=\sqrt{12\left(12-5\right)\left(12-8\right)\left(12-11\right)} \\ A=4\sqrt{21}$$