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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