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

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Answer 1 · 2016-01-24T22:39:05

#A=2sqrt21approx9.1652#

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+5+5)/2=7#

which gives an area of

#A=sqrt(7(7-4)(7-5)(7-5))#

#A=sqrt(7xx3xx2xx2)#

#A=2sqrt21approx9.1652#