How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #5 #, and #6 #?

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Answer 1 · 2016-01-30T21:41:09

#A = sqrt(s(s-a)(s-b)(s-c)) = 6sqrt(6) ~~ 14.6969#

Heron's formula tells us that the area #A# of a triangle with sides of length #a#, #b# and #c# is given by the formula:

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

Where #s = (a+b+c)/2# is the semi-perimeter

In our case, let #a=7#, #b=5# and #c=6#.

Then #s = (a+b+c)/2 = (7+5+6)/2 = 9# and we find:

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

#=sqrt(9 * (9-7) * (9-5) * (9-6))#

#=sqrt(9*2*4*3)#

#= sqrt(36*6) = sqrt(36)*sqrt(6) = 6sqrt(6) ~~ 14.6969#