How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #5 #, and #8 #?

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Answer 1 · 2016-01-25T13:33:22

#10sqrt3# #sq.cm^2#

Use Heron's formula:-
#sqrt[s(s-a)(s-b)(s-c)]#
Where #s#=semi-perimeter of triangle=#(a+b+c)/2#

So,#a=7,b=5,c=8,s=10=(7+5+8)/2=20/2#

#rarrsqrt[s(s-a)(s-b)(s-c)]#

#rarrsqrt[10(10-7)(10-5)(10-8)]#

#rarrsqrt[10(3)(5)(2)]#

#rarrsqrt[10(30)]#

#rarrsqrt300=10sqrt3#