How do you use Heron's formula to find the area of a triangle with sides of lengths #6 #, #4 #, and #9 #?

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Answer 1 · 2016-03-10T02:03:50

#frac{sqrt{1463}}{4} ~~ 9.562#

For a triangle with side #a#, #b# and #c#, we first calculate the semi-perimeter, which is half of the perimeter of the triangle.

#s = frac{a+b+c}{2}#

Heron's formula states that the area of the triangle is given by

#"Area" = sqrt{s(s-a)(s-b)(s-c)}#

In this question, we have

The semi-perimeter, #s#, is

#s = frac{6+4+9}{2} = 19/2#

So, the area of the triangle is

#"Area" = sqrt{19/2(19/2-6)(19/2-4)(19/2-9)}#

#= frac{sqrt{1463}}{4}#

#~~ 9.562#