How do you use Heron's formula to find the area of a triangle with sides of lengths $1$ , $7$ , and $7$ ?

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Answer 1 · 2016-01-29T15:25:39

$Area=3.49106001$ 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 $a=1, b=7$ and $c=7$

$implies s=(1+7+7)/2=15/2=7.5$

$implies s=7.5$

$implies s-a=7.5-1=6.5, s-b=7.5-7=0.5 and s-c=7.5-7=0.5$
$implies s-a=6.5, s-b=0.5 and s-c=0.5$

$implies Area=sqrt(7.5*6.5*0.5*0.5)=sqrt12.1875=3.491060011$ square units

$implies Area=3.49106001$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 1 1 , 7 7 , and 7 7 ?