How do you use Heron's formula to find the area of a triangle with sides of lengths $5$ , $6$ , and $7$ ?

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Answer 1 · 2016-02-01T23:03:20

$"A"=14.7 "square units"$ (rounded to one decimal place)

$"A"=sqrt(s(s-a)(s-b)(s-c)$ , where $s$ is the semiperimeter.

The semiperimeter is the perimeter divided by 2, $s=(a+b+c)/2$ .

Let side $a=5$ , side $b=6$ , and side $c=7$ .

$s=(5+6+7)/2$

$s=18/2$

$s=9$

Substitute the known values into Heron's formula.

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

$"A"=sqrt(9(9-5)(9-6)(9-7)$

Simplify.

$"A"=sqrt(9(4)(3)(2))$

$"A"=sqrt(216)$

$"A"=14.7 "square units"$ (rounded to one decimal place)

How do you use Heron's formula to find the area of a triangle with sides of lengths 5 5 , 6 6 , and 7 7 ?