A triangle has sides with lengths: 7, 2, and 15. How do you find the area of the triangle using Heron's formula?

1 Answer
Deepak G.
Jul 31, 2016

#=42.43#

Explanation:

As per Heron's formula
Area of a triangle with sides #a#;#b#; and # c#
#A=sqrt(s(s-a)(s-b)(s-c))#
where #s# is half perimeter of the triangle and is given by
#s=(a+b+c)/2#
So we have
#a=7# ;#b=2# and #c=15#
Therefore Perimeter of the triangle
#s=(7+2+15)/2#
or
#s=24/2#
or
#s=12#
Area of the triangle
#A=sqrt(s(s-a)(s-b)(s-c))#
#=sqrt(12(12-7)(12-2)(12-15))#
#=sqrt(12(5)(10)(3)#
#=sqrt1800#
#=42.43#

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