# 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#