How do you use Heron's formula to find the area of a triangle with sides of lengths #29 #, #25 #, and #12 #?

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Answer 1 · 2016-06-20T09:39:46

Area of triangle is #148.92#

If the sides of a triangle are #a#, #b# and #c#, then according to Heron's formula, the area of the triangle is given by the formula

#Delta=sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#

Now given the sides of a triangle as #29#, #25# and #12#

#s=1/2xx(29+25+12)=1/2xx66=33# and

#Delta=sqrt(33(33-29)(33-25)(33-12))#

= #sqrt(33xx4xx8xx21)#

= #sqrt(3xx11xx2xx2xx2xx2xx2xx3xx7)#

= #3xx2xx2sqrt(11xx2xx7)=12sqrt154=12xx12.41=148.92#