How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #4 #, and #5 #?

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Answer 1 · 2016-01-24T22:36:53

#A=(5sqrt39)/4approx7.806#

Heron's formula states that for a triangle with sides #a,b,c# and a semiperimeter #s=(a+b+c)/2#, the area of the triangle is

#A=sqrt(s(s-a)(s-b)(s-c))#

Here, we know that

#s=(4+4+5)/2=13/2#

which gives an area of

#A=sqrt(13/2(13/2-4)(13/2-4)(13/2-5))#

#A=sqrt(13/2(5/2)(5/2)(3/2))#

#A=sqrt((39xx5^2)/4^2)#

#A=(5sqrt39)/4approx7.806#