How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ , $5$ , and $5$ ?

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Answer 1 · 2016-01-24T22:39:05

$A=2sqrt21approx9.1652$

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

$s=(4+5+5)/2=7$

which gives an area of

$A=sqrt(7(7-4)(7-5)(7-5))$

$A=sqrt(7xx3xx2xx2)$

$A=2sqrt21approx9.1652$

How do you use Heron's formula to find the area of a triangle with sides of lengths 4 4 , 5 5 , and 5 5 ?