# Compute 4

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

Correct result:

S =  68.228 mi2

#### Solution:

$a=14 \ \text{mi} \ \\ b=12 \ \text{mi} \ \\ c=12 \ \text{mi} \ \\ \ \\ s=\dfrac{ a+b+c }{ 2 }=\dfrac{ 14+12+12 }{ 2 }=19 \ \text{mi} \ \\ \ \\ S=\sqrt{ s \cdot \ (s-a) \cdot \ (s-b) \cdot \ (s-c) }=\sqrt{ 19 \cdot \ (19-14) \cdot \ (19-12) \cdot \ (19-12) }=7 \ \sqrt{ 95 }=68.228 \ \text{mi}^2$

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