# How do you use Heron's formula to determine the area of a triangle with sides of that are 4, 6, and 3 units in length?

##### 1 Answer
Apr 27, 2016

${\text{Area}}_{\triangle} \approx 5.3$ sq.units
(see below for use of Heron's formula)

#### Explanation:

Heron's formula tells us how to calculate the area of a triangle given the lengths of it's three sides.

If (for the general case) the lengths of the three sides are $a , b , \mathmr{and} c$ and the semi-perimeter is $s = \frac{a + b + c}{2}$

Then
color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))

For the given triangle with sides $4 , 6 , \mathmr{and} 3$
$\textcolor{w h i t e}{\text{XXX}} s = \frac{13}{2}$
and
color(white)("XXX")"Area"_triangle = sqrt((13/2)(13/2-4)(13/2-6)(13/2-3))

$\textcolor{w h i t e}{\text{XXXXXXX}} = \sqrt{\frac{13}{2} \times \frac{5}{2} \times \frac{1}{2} \times \frac{7}{2}}$

$\textcolor{w h i t e}{\text{XXXXXXX}} = \frac{\sqrt{455}}{4}$

$\textcolor{w h i t e}{\text{XXXXXXX}} \approx 5.3$ sq.units