Compute 4

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

Result

S =  68.228 mi2

Solution:

a=14 mi b=12 mi c=12 mi  s=a+b+c2=14+12+122=19 mi  S=s⋅ (s−a)⋅ (s−b)⋅ (s−c)=19⋅ (19−14)⋅ (19−12)⋅ (19−12)≐7 95≐68.2276≐68.228 mi2a=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) } \doteq 7 \ \sqrt{ 95 } \doteq 68.2276 \doteq 68.228 \ \text{mi}^2

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It made it easier to explain to my 6th grader.  I'm hoping he continues using your service it's explainable and understandable for kids.

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