How do you use Heron's formula to find the area of a triangle with sides of lengths #15 #, #16 #, and #12 #?

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Answer 1 · 2016-01-23T16:17:59

#Area=85.45137# 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=15, b=16# and #c=12#

#implies s=(15+16+12)/2=43/2=21.5#

#implies s=21.5#

#implies s-a=21.5-15=6.5, s-b=21.5-16=5.5 and s-c=21.5-12=9.5#
#implies s-a=6.5, s-b=5.5 and s-c=9.5#

#implies Area=sqrt(21.5*6.5*5.5*9.5)=sqrt7301.9375=85.45137# square units

#implies Area=85.45137# square units