How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 16, and 17 units in length?

1 Answer
Apr 10, 2016

=104.324 square units

Explanation:

Heron's formula for area of triangle is:

A = sqrt(s(s-a)(s-b)(s-c), where s is the semi-pertimeter.

=>s=(a+b+c)/2

Here, a=14, b=16 and c=17.

First find s:

s=(a+b+c)/2

=(14+16+17)/2=47/2

Now to calculate the area:

A = sqrt(s(s-a)(s-b)(s-c)

= sqrt(47/2(47/2-14)(47/2-16)(47/2-17)

= sqrt(47/2((47-28)/2)((47-32)/2)((47-34)/2)

= sqrt(47/2(19/2)(15/2)(13/2)

=sqrt((47xx19xx15xx13)/16)

=1/4sqrt(47xx19xx15xx13)

=1/4sqrt(174135)

=1/4xx417.294

=104.324