How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 9 units in length?

1 Answer
Steve M
Mar 19, 2018

# 9.56 \ 2 \ dp#

Explanation:

Heron's Formula tells us that given all three sides of a triangle, #a,b,c#, say, then the area of the triangle is given by:

# A = sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#

So, for the given triangle we have:

# s=1/2(6+4+9) = 19/2 #

And so we get:

# A = sqrt(19/2(19/2-6)(19/2-4)(19/2-9))#
# \ \ \ = sqrt(19/2(7/2)(11/2)(1/2))#
# \ \ \ = sqrt(1463/16)#
# \ \ \ = sqrt(1463)/4#
# \ \ \ = 9.562295 ...#
# \ \ \ = 9.56 \ 2 \ dp#

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