How do you use Heron's formula to find the area of a triangle with sides of lengths #9 #, #5 #, and #12 #?

1 Answer
Jan 25, 2016

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=5# and #c=12#

#implies s=(9+5+12)/2=26/2=13#

#implies s=13#

#implies s-a=13-9=4, s-b=13-5=8 and s-c=13-12=1#
#implies s-a=4, s-b=8 and s-c=1#

#implies Area=sqrt(13*4*8*1)=sqrt416=20.396# square units

#implies Area=20.396# square units