How do you use Heron's formula to find the area of a triangle with sides of lengths #9 #, #4 #, and #8 #?

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Answer 1 · 2016-01-25T02:56:06

#Area=15.998# 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=9, b=4# and #c=8#

#implies s=(9+4+8)/2=21/2=10.5#

#implies s=10.5#

#implies s-a=10.5-9=1.5, s-b=10.5-4=6.5 and s-c=10.5-8=2.5#
#implies s-a=1.5, s-b=6.5 and s-c=2.5#

#implies Area=sqrt(10.5*1.5*6.5*2.5)=sqrt255.9375=15.998# square units

#implies Area=15.998# square units