What is the area of a triangle with sides of length 2, 6, and 5?

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Answer 1 · 2016-03-14T01:27:46

Apply Heron's formula to find the area to be

#sqrt(351)/4~~4.6837#

Heron's formula states that, given a triangle with side lengths #a, b, c# and semiperimeter #s = (a+b+c)/2# the area #A# of the triangle is

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

In this case, we have #a = 2#, #b = 6#, and #c = 5#. Then, for this triangle we have #s = (2+6+5)/2 = 13/2#. Applying Heron's formula gives us

#A = sqrt(13/2(13/2-2)(13/2-6)(13/2-5))#

#=sqrt(13/2*9/2*1/2*3/2)#

#=sqrt(351/16)#

#=sqrt(351)/4~~4.6837#