Question 247152
<pre><font size = 4 color = "indigo"><b>
Hero(n)'s formula states that a triangle that has sides a,b,c, has area:

{{{A=sqrt(s(s-a)(s-b)(s-c))}}}

where {{{s=semiperimeter=perimeter/2=(a+b+c)/2}}}

Just substitute {{{a=5}}}, {{{b=6}}}, and {{{c=7}}}

{{{s=semiperimeter=perimeter/2=(a+b+c)/2=(5+6+7)/2=18/2=9}}}

Then substitute {{{a=5}}}, {{{b=6}}}, {{{c=7}}}, and {{{s=9}}} in

{{{A=sqrt(s(s-a)(s-b)(s-c))}}}

{{{A=sqrt(9(9-5)(9-6)(9-7))}}}

{{{A=sqrt(9(4)(3)(2))}}}

{{{A=3*2*sqrt(3*2)}}}

{{{A=6*sqrt(6)}}}, which is about 14.69693846

Edwin</pre>