Compute 4

Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long.

Correct answer:

S =  68.2276 mi²

Step-by-step explanation:

$$\begin{gathered} a=14\text{ mi } \\ b=12\text{ mi } \\ c=12\text{ mi } \\ s={\displaystyle \frac{a+b+c}{2}}={\displaystyle \frac{14+12+12}{2}}=19\text{ mi } \\ S=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{19\cdot (19-14)\cdot (19-12)\cdot (19-12)}=7\sqrt{95}=68.2276{\text{mi}}^2 \end{gathered}$$

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