Chapter 6 - Section 6.6 - The Law of Cosines - 6.6 Exercises - Page 521: 32

$10\sqrt{3021}$

In order to use Heron's Formula we have to find the semiperimeter: $s=\frac{1}{2}(a+b+c)$ $s=\frac{1}{2}(11+100+101)$ $s=\frac{1}{2}*212$ $s=106$ We can use Heron's Formula from here: $A=\sqrt{s(s-a)(s-b)(s-c)}$ $A=\sqrt{106*(106-11)(106-100)(106-101)}$ $A=\sqrt{106*95*6*5}$ $A=\sqrt{302100}$ $A=10\sqrt{3021}$ $A\approx 549.64$