How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ , $6$ , and $3$ ?

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Answer 1 · 2016-01-22T19:17:41

$Area=5.33268$ square units

Hero'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 $a=4, b=6$ and $c=3$

$implies s=(4+6+3)/2=13/2=6.5$

$implies s=6.5$

$implies s-a=6.5-4=2.5, s-b=6.5-6=0.5 and s-c=6.5-3=3.5$
$implies s-a=2.5, s-b=0.5 and s-c=3.5$

$implies Area=sqrt(6.5*2.5*0.5*3.5)=sqrt28.4375=5.33268$ square units

$implies Area=5.33268$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 4 4 , 6 6 , and 3 3 ?