How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 6, and 7 units in length?

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Answer 1 · 2016-01-23T18:13:32

$Area=20.976$ 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 $a=9, b=6$ and $c=7$

$implies s=(9+6+7)/2=22/2=11$

$implies s=11$

$implies s-a=11-9=2, s-b=11-6=5 and s-c=11-7=4$
$implies s-a=2, s-b=5 and s-c=4$

$implies Area=sqrt(11*2*5*4)=sqrt440=20.976$ square units

$implies Area=20.976$ square units