How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #7 #?

1 Answer
Jan 23, 2016

#"Area"_triangle = 6sqrt(5)#

Explanation:

Heron's formula says that for a triangle with sides of length #a, b, c# and semi-perimeter #s=(a+b+c)/2#

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

For the specified triangle
#color(white)("XXX")a=7#
#color(white)("XXX")b=4#
#color(white)("XXX")c=7#
#rarrcolor(white)("XXX")s=9#

#"Area"_triangle = sqrt(9(2)(5)(2)) = sqrt(3^3xx2^2xx5) = 6sqrt(5)#