How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #6 #, and #3 #?

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Answer 1 · 2016-01-22T19:17:41

#Area=5.33268# square units

Hero'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=4, b=6# and #c=3#

#implies s=(4+6+3)/2=13/2=6.5#

#implies s=6.5#

#implies s-a=6.5-4=2.5, s-b=6.5-6=0.5 and s-c=6.5-3=3.5#
#implies s-a=2.5, s-b=0.5 and s-c=3.5#

#implies Area=sqrt(6.5*2.5*0.5*3.5)=sqrt28.4375=5.33268# square units

#implies Area=5.33268# square units