# 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?

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.

$\implies s = \frac{a + b + c}{2}$

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

First find $s$:

$s = \frac{a + b + c}{2}$

$= \frac{14 + 16 + 17}{2} = \frac{47}{2}$

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)

$= \sqrt{\frac{47 \times 19 \times 15 \times 13}{16}}$

$= \frac{1}{4} \sqrt{47 \times 19 \times 15 \times 13}$

$= \frac{1}{4} \sqrt{174135}$

$= \frac{1}{4} \times 417.294$

$= 104.324$