How do you use Heron's formula to find the area of a triangle with sides of lengths #5 #, #6 #, and #7 #?

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Answer 1 · 2016-02-01T23:03:20

#"A"=14.7 "square units"# (rounded to one decimal place)

#"A"=sqrt(s(s-a)(s-b)(s-c)#, where #s# is the semiperimeter.

The semiperimeter is the perimeter divided by 2, #s=(a+b+c)/2#.

Let side #a=5#, side #b=6#, and side #c=7#.

#s=(5+6+7)/2#

#s=18/2#

#s=9#

Substitute the known values into Heron's formula.

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

#"A"=sqrt(9(9-5)(9-6)(9-7)#

Simplify.

#"A"=sqrt(9(4)(3)(2))#

#"A"=sqrt(216)#

#"A"=14.7 "square units"# (rounded to one decimal place)