How do you use Heron's formula to find the area of a triangle with sides of lengths #9 #, #3 #, and #9 #?

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Answer 1 · 2016-01-24T22:50:54

#A=(9sqrt35)/4approx13.3112#

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=(9+3+9)/2=21/2#

which gives an area of

#A=sqrt(21/2(21/2-9)(21/2-3)(21/2-9))#

#A=sqrt(21/2(3/2)(15/2)(3/2))#

#A=sqrt((9^2xx7xx5)/4^2)#

#A=(9sqrt35)/4approx13.3112#