How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #5 #, and #8 #?

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Answer 1 · 2016-01-24T16:21:51

#Area=14.52369# 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=12, b=5# and #c=8#

#implies s=(12+5+8)/2=25/2=12.5#

#implies s=12.5#

#implies s-a=12.5-12=0.5, s-b=12.5-5=7.5 and s-c=12.5-8=4.5#
#implies s-a=0.5, s-b=7.5 and s-c=4.5#

#implies Area=sqrt(12.5*0.5*7.5*4.5)=sqrt210.9375=14.52369# square units

#implies Area=14.52369# square units