How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #6 #, and #5 #?

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Answer 1 · 2016-01-29T19:25:14

The area is:

#A~~9.92# square units

The Heron's Formula says that for any triangle with sides #a,b# and #c# its area can be calculated as:

#A=sqrt(p(p-a)(p-b)(p-c))#

where:

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

So to calculate the area we calculate:

#p=(4+5+6)/2=7.5#

#p-a=7.5-4=3.5#

#p-b=7.5-5=2.5#

#p-c=7.5-6=1.5#

Now we can write that:

#A=sqrt(7.5*3.5*2.5*1.5)#

#A=sqrt(98.4375)#

#A~~9.92#

Answer: The area is approximately #9.92# square units