##### Question 11.2.13

Show that the area of a triangle with side lengths $a$, $b$, and $c$ is: $A = \sqrt{s(s-a)(s-b)(s-c)}$ where $s$ is the semiperimeter (half the perimeter): $s = \frac{a + b + c}{2}.$ This is called Heron’s formula, after the ancient mathematician Heron (or Hero) of Alexandria. Show hint