How do you use Heron's formula to find the area of a triangle with sides of lengths $14$ , $9$ , and $13$ ?

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Answer 1 · 2018-05-27T11:13:46

$color(blue)("Area"=18sqrt(10)" square units")$

$"Area=sqrt(s(s-a)(s-b)(s-c))$

Where $a, b and c$ are the lengths of the triangles sides.

$s="semiperimeter"=(a+b+c)/2$

Let: $a=14$ , $b=13$ . $c=9$

Then:

$s=(14+13+9)/2=$ 18

$"Area"=sqrt(18(18-14)(18-13)(18-9))$

$\ \ \ \ \ \ \ \ \ =sqrt(18(4)(5)(9)$

$\ \ \ \ \ \ \ \ \ =sqrt(3240)=18sqrt(10)$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 14 14 , 9 9 , and 13 13 ?