How do you use Heron's formula to find the area of a triangle with sides of lengths #3 #, #3 #, and #4 #?

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Answer 1 · 2016-01-30T12:57:27

#Area=4.47213# square units

Heron's formula for finding area of the triangle is given by
#Area=sqrt(s(s-a)(s-b)(s-c))#

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

and #a, b, c# are the lengths of the three sides of the triangle.

Here let #a=3, b=3# and #c=4#

#implies s=(3+3+4)/2=10/2=5#

#implies s=5#

#implies s-a=5-3=2, s-b=5-3=2 and s-c=5-4=1#
#implies s-a=2, s-b=2 and s-c=1#

#implies Area=sqrt(5*2*2*1)=sqrt20=4.47213# square units

#implies Area=4.47213# square units