How do you use Heron's formula to find the area of a triangle with sides of lengths $4$ , $6$ , and $5$ ?

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Answer 1 · 2016-01-29T19:25:14

The area is:

$A~~9.92$ square units

The Heron's Formula says that for any triangle with sides $a,b$ and $c$ its area can be calculated as:

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

where:

$p=(a+b+c)/2$ .

So to calculate the area we calculate:

$p=(4+5+6)/2=7.5$

$p-a=7.5-4=3.5$

$p-b=7.5-5=2.5$

$p-c=7.5-6=1.5$

Now we can write that:

$A=sqrt(7.5*3.5*2.5*1.5)$

$A=sqrt(98.4375)$

$A~~9.92$

Answer: The area is approximately $9.92$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 4 4 , 6 6 , and 5 5 ?