How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #9 #?

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Answer 1 · 2016-01-24T22:59:08

#A=6sqrt5approx13.4164#

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=(7+4+9)/2=10#

which gives an area of

#A=sqrt(10(10-7)(10-4)(10-9)#

#A=sqrt(10xx3xx6xx1)#

#A=6sqrt5approx13.4164#