How do you use Heron's formula to find the area of a triangle with sides of lengths #8 #, #3 #, and #9 #?

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Answer 1 · 2016-02-04T07:59:30

#A~~11.8"# square units rounded to one decimal place.

Heron's formula for the area of a triangle is #A=sqrt(s(s-a)(s-b)(s-c))#, where #s# is the semiperimeter, which is half the perimeter.

#s=(a+b+c)/2#, where #a=8, b=3, and c=9#.

#s=(8+3+9)/2#

Simplify.

#s=20/2#

#s=10#

Heron's Formula

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

Substitute the known values into the equation and solve.

#A=sqrt(10(10-8)(10-3)(10-9)#

Simplify.

#A=sqrt((10)(2)(7)(1))#

#A=sqrt140#

#A~~11.8"# square units rounded to one decimal place.