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
Mar 19, 2018
# 9.56 \ 2 \ dp#
Explanation:
Heron's Formula tells us that given all three sides of a triangle,
# 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#
