How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #9 #, and #15 #?

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Answer 1 · 2016-01-25T16:53:49

# Area=61.644# 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=14, b=9# and #c=15#

#implies s=(14+9+15)/2=38/2=19#

#implies s=19#

#implies s-a=19-14=5, s-b=19-9=10 and s-c=19-15=4#
#implies s-a=5, s-b=10 and s-c=4#

#implies Area=sqrt(19*5*10*4)=sqrt3800=61.644# square units

#implies Area=61.644# square units