How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #5 #, and #7 #?

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Answer 1 · 2016-01-22T19:22:53

#Area=16.34587# 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=7, b=5# and #c=7#

#implies s=(7+5+7)/2=19/2=9.5#

#implies s=9.5#

#implies s-a=9.5-7=2.5, s-b=9.5-5=4.5 and s-c=9.5-7=2.5#
#implies s-a=2.5, s-b=4.5 and s-c=2.5#

#implies Area=sqrt(9.5*2.5*4.5*2.5)=sqrt267.1875=16.34587# square units

#implies Area=16.34587# square units