How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 6, and 13 units in length?

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Answer 1 · 2016-01-23T18:16:58

$Area=38.678$ square units

Heron's formula for finding area of the triangle is given by
$Area=sqrt(s(s-a)(s-b)(s-c))$

Where $s$ is the semi perimeter and is defined as
$s=(a+b+c)/2$

and $a, b, c$ are the lengths of the three sides of the triangle.

Here let $a=15, b=6$ and $c=13$

$implies s=(15+6+13)/2=34/2=17$

$implies s=17$

$implies s-a=17-15=2, s-b=17-6=11 and s-c=17-13=4$
$implies s-a=2, s-b=11 and s-c=4$

$implies Area=sqrt(17*2*11*4)=sqrt1496=38.678$ square units

$implies Area=38.678$ square units