How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #6 #, and #8 #?

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Answer 1 · 2016-01-25T03:19:50

#Area=21.33# square units

Heron's formula for finding area of the triangle is given by
#Area=sqrt(s(s-a)(s-b)(s-c))#

Where #s# is the semi perimeter and is defined as
#s=(a+b+c)/2#

and #a, b, c# are the lengths of the three sides of the triangle.

Here let #a=12, b=6# and #c=8#

#implies s=(12+6+8)/2=26/2=13#

#implies s=13#

#implies s-a=13-12=1, s-b=13-6=7 and s-c=13-8=5#
#implies s-a=1, s-b=7 and s-c=5#

#implies Area=sqrt(13*1*7*5)=sqrt455=21.33# square units

#implies Area=21.33# square units