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