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

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Answer 1 · 2016-01-21T20:56:06

Use Heron's formula to find area #A=4sqrt(26) ~~ 20.396#

Heron's formula gives the area #A# of the triangle in terms of its sides #a#, #b#, #c# and semi-perimeter #s = (a+b+c)/2# as:

#A = sqrt(s(s-a)(s-b)(s-c))#

In our example, #a=9#, #b=5#, #c=12#, #s = (a+b+c)/2 = 13# and:

#A = sqrt(s(s-a)(s-b)(s-c))#

#= sqrt(13*4*8*1) = sqrt(416) = 4sqrt(26) ~~ 20.396#