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

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Answer 1 · 2016-01-25T02:48:59

#Area=0.433# 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=1# and #c=1#

#implies s=(1+1+1)/2=3/2=1.5#

#implies s=1.5#

#implies s-a=1.5-1=2, s-b=1.5-1=0.5 and s-c=1.5-1=0.5#
#implies s-a=0.5, s-b=0.5 and s-c=0.5#

#implies Area=sqrt(1.5*0.5*0.5*0.5)=sqrt0.1875=0.433# square units

#implies Area=0.433# square units