How do you use Heron's formula to find the area of a triangle with sides of lengths $7$ , $5$ , and $7$ ?

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Answer 1 · 2016-01-22T19:22:53

$Area=16.34587$ 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 $a=7, b=5$ and $c=7$

$implies s=(7+5+7)/2=19/2=9.5$

$implies s=9.5$

$implies s-a=9.5-7=2.5, s-b=9.5-5=4.5 and s-c=9.5-7=2.5$
$implies s-a=2.5, s-b=4.5 and s-c=2.5$

$implies Area=sqrt(9.5*2.5*4.5*2.5)=sqrt267.1875=16.34587$ square units

$implies Area=16.34587$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 7 7 , 5 5 , and 7 7 ?