How do you use Heron's formula to find the area of a triangle with sides of lengths #1 #, #5 #, and #5 #?

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Answer 1 · 2016-01-25T03:07:43

#Area=2.48746# 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=5# and #c=5#

#implies s=(1+5+5)/2=11/2=5.5#

#implies s=5.5#

#implies s-a=5.5-1=4.5, s-b=5.5-5=0.5 and s-c=5.5-5=0.5#
#implies s-a=4.5, s-b=0.5 and s-c=0.5#

#implies Area=sqrt(5.5*4.5*0.5*0.5)=sqrt6.1875=2.48746# square units

#implies Area=2.48746# square units