How do you use Heron's formula to find the area of a triangle with sides of lengths #1 #, #7 #, and #7 #?

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Answer 1 · 2016-01-29T15:25:39

#Area=3.49106001# 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=1, b=7# and #c=7#

#implies s=(1+7+7)/2=15/2=7.5#

#implies s=7.5#

#implies s-a=7.5-1=6.5, s-b=7.5-7=0.5 and s-c=7.5-7=0.5#
#implies s-a=6.5, s-b=0.5 and s-c=0.5#

#implies Area=sqrt(7.5*6.5*0.5*0.5)=sqrt12.1875=3.491060011# square units

#implies Area=3.49106001# square units