How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #9 #, and #13 #?

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Answer 1 · 2018-05-27T11:13:46

#color(blue)("Area"=18sqrt(10)" square units")#

#"Area=sqrt(s(s-a)(s-b)(s-c))#

Where #a, b and c# are the lengths of the triangles sides.

#s="semiperimeter"=(a+b+c)/2#

Let: #a=14#, #b=13#. #c=9#

Then:

#s=(14+13+9)/2=#18

#"Area"=sqrt(18(18-14)(18-13)(18-9))#

# \ \ \ \ \ \ \ \ \ =sqrt(18(4)(5)(9)#

# \ \ \ \ \ \ \ \ \ =sqrt(3240)=18sqrt(10) # square units