Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - Guided Practice for Example 4 - Page 891: 5

$$A=6\sqrt{5}$$

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: $$s=\frac{7+4+9}{2}=10\\ A=\sqrt{10\left(10-7\right)\left(10-4\right)\left(10-9\right)} \\ A=6\sqrt{5}$$