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

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Answer 1 · 2016-02-14T22:34:21

The area is approximately #A~~25.18#

Heron's formula says that for any triangle its area can be calculated as
#A=sqrt(p(p-a)(p-b)(p-c))#

where #p=(a+b+c)/2#

so for this example we have:

#p=(7+8+8)/2=23/2=11.5#

#p-a=11.5-7=4.5#

#p-b=p-c=11.5-8=3.5#

so the area is:

#A=sqrt(11.5*4.5*3.5*3.5)#

#A=sqrt(633.9379)#

#A~~25.18#