How do you use Heron's formula to find the area of a triangle with sides of lengths $7$ , $4$ , and $9$ ?

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Answer 1 · 2016-01-24T22:59:08

$A=6sqrt5approx13.4164$

Heron's formula states that for a triangle with sides $a,b,c$ and a semiperimeter $s=(a+b+c)/2$ , the area of the triangle is

$A=sqrt(s(s-a)(s-b)(s-c))$

Here, we know that

$s=(7+4+9)/2=10$

which gives an area of

$A=sqrt(10(10-7)(10-4)(10-9)$

$A=sqrt(10xx3xx6xx1)$

$A=6sqrt5approx13.4164$

How do you use Heron's formula to find the area of a triangle with sides of lengths 7 7 , 4 4 , and 9 9 ?