How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #8 #, and #15 #?

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Answer 1 · 2016-01-21T08:37:58

#Area=55.31218# 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=14, b=8# and #c=15#

#implies s=(14+8+15)/2=37/2=18.5#

#implies s=18.5#

#implies s-a=18.5-14=4.5, s-b=18.5-8=10.5 and s-c=18.5-15=3.5#

#implies s-a=4.5, s-b=10.5 and s-c=3.5#

#implies Area=sqrt(18.5*4.5*10.5*3.5)=sqrt3059.4375=55.31218# square units

#implies Area=55.31218# square units