A triangle has sides with lengths: 4, 12, and 2. How do you find the area of the triangle using Heron's formula?

1 Answer
Alan P.
Jan 16, 2016

No such triangle is possible since no triangle can have a side which is longer than the sum of the other two sides (at least in Euclidean space)

Explanation:

If you attempted to apply Heron's formula:
#color(white)("XXX")Area = sqrt(s(s-a)(s-b)(s-c))#
for a triangle with sides #a=4, b=12, c=2#
and semi-perimeter #s=9# (i.e. #(a+b+c)/2#)

you would end up attempting to find the square root of a negative number: #sqrt(9 * (5) * (-3) * (7))#

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