How do you use Heron's formula to find the area of a triangle with sides of lengths #3 #, #5 #, and #5 #?

1 Answer
Alan P.
Jan 27, 2016

#"Area"_triangle=7/4sqrt(39)#

Explanation:

Given sides #(a,b,c) = (3,3,5)#
the semi-perimeter is #s=(3+3+5)/2 = 13/2#

and by Heron's formula: #"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))#

So
#color(white)("XXX")"Area"_triangle = sqrt(13/2xx7/2xx7/2xx3/2)#

#color(white)("XXXXXXX")=sqrt((13xx3xx7^2)/(4^2))#

#color(white)("XXXXXX")=7/4sqrt(39)#

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