How do you use Heron's formula to find the area of a triangle with sides of lengths #11 #, #14 #, and #18 #?

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Answer 1 · 2016-01-22T23:54:49

#Area=76.98# 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=11, b=14# and #c=18#

#implies s=(11+14+18)/2=43/2=21.5#

#implies s=21.5#

#implies s-a=21.5-11=10.5, s-b=21.5-14=7.5 and s-c=21.5-18=3.5#
#implies s-a=10.5, s-b=7.5 and s-c=3.5#

#implies Area=sqrt(21.5*10.5*7.5*3.5)=sqrt5925.9375=76.98# square units

#implies Area=76.98# square units