How do you use Heron's formula to find the area of a triangle with sides of lengths $7$ , $4$ , and $8$ ?

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Answer 1 · 2016-01-21T19:47:35

$Area=13.99777$ 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 $a=7, b=4$ and $c=8$

$implies s=(7+4+8)/2=19/2=9.5$

$implies s=9.5$

$implies s-a=9.5-7=2.5, s-b=9.5-4=5.5 and s-c=9.5-8=1.5$
$implies s-a=2.5, s-b=5.5 and s-c=1.5$

$implies Area=sqrt(9.5*2.5*5.5*1.5)=sqrt195.9375=13.99777$ square units

$implies Area=13.99777$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 7 7 , 4 4 , and 8 8 ?