How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 31 units in length?

1 Answer
George C.
Dec 26, 2015

Substitute the values into Heron's formula to find:

#A = sqrt(109956) ~~ 331.59614#

Explanation:

Heron's formula can be written:

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

where #A# is the area, #a#, #b#, #c# are the lengths of the sides and

#sp = (a+b+c)/2 color(white)(X)# is the semi-perimeter.

In our example, #a=25#, #b=28#, #c=31#

#sp = (a+b+c)/2 = (25+28+31)/2 = 84/2 = 42#

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

#=sqrt(42(42-25)(42-28)(42-31))#

#=sqrt(42*17*14*11)#

#=sqrt(109956) ~~ 331.59614#

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