6. A triangle has side lengths $7,11,14$. Find the length of its inradius.
Answer: $\frac{3 \sqrt{10}}{4}$
Solution: We use Heron's formula. The semiperimeter of the triangle is 16 . Thus, the area of the triangle is $\sqrt{(16)(16-7)(16-11)(16-2)}=12 \sqrt{10}$. Since the area of a triangle is the product of the semiperimeter and the inradius, the length of the inradius is $\frac{3 \sqrt{10}}{4}$