How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #8 #, and #11 #?

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Answer 1 · 2016-01-25T03:13:59

#Area=42.7894# 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=8# and #c=11#

#implies s=(12+8+11)/2=31/2=15.5#

#implies s=15.5#

#implies s-a=15.5-12=3.5, s-b=15.5-8=7.5 and s-c=15.5-11=4.5#
#implies s-a=3.5, s-b=7.5 and s-c=4.5#

#implies Area=sqrt(15.5*3.5*7.5*4.5)=sqrt1830.9375=42.7894# square units

#implies Area=42.7894# square units