How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 3, and 7 units in length?

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Answer 1 · 2016-01-22T18:38:01

$Area=8.7856$ 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 $a=9, b=3$ and $c=7$

$implies s=(9+3+7)/2=19/2=9.5$

$implies s=9.5$

$implies s-a=9.5-9=0.5, s-b=9.5-3=6.5 and s-c=9.5-7=2.5$
$implies s-a=0.5, s-b=6.5 and s-c=2.5$

$implies Area=sqrt(9.5*0.5*6.5*2.5)=sqrt77.1875=8.7856$ square units

$implies Area=8.7856$ square units