How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 15, and 10 units in length?

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Answer 1 · 2016-01-11T08:02:21

$Area=43.6348$ 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 $a=9, b=15$ and $c=10$

$implies s=(9+15+10)/2=34/2=17$

$implies s=17$

$implies s-a=17-9=8, s-b=2 and s-c=7$

$implies s-a=8, s-b=2 and s-c=7$

$implies Area=sqrt(17*8*2*7)=sqrt1904=43.6348$ square units

$implies Area=43.6348$ square units