How do you use Heron's formula to find the area of a triangle with sides of lengths #18 #, #7 #, and #19 #?

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Answer 1 · 2016-01-23T19:07:39

#Area=62.9285# 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=18, b=7# and #c=19#

#implies s=(18+7+19)/2=44/2=22#

#implies s=22#

#implies s-a=22-18=4, s-b=22-7=15 and s-c=22-19=3#
#implies s-a=4, s-b=15 and s-c=3#

#implies Area=sqrt(22*4*15*3)=sqrt3960=62.9285# square units

#implies Area=62.9285# square units