How do you use Heron's formula to find the area of a triangle with sides of lengths $1$ , $2$ , and $2$ ?

Question

3307 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-29T15:19:23

$Area=0.9682458366$ square units

enter image source here
Heron's formula for finding area of the triangle is given by
$Area=sqrt(s(s-a)(s-b)(s-c))$

Where $s$ is the semi perimeter and is defined as
$s=(a+b+c)/2$

and $a, b, c$ are the lengths of the three sides of the triangle.

Here let $a=1, b=2$ and $c=2$

$implies s=(1+2+2)/2=5/2=2.5$

$implies s=2.5$

$implies s-a=2.5-1=1.5, s-b=2.5-2=0.5 and s-c=2.5-2=0.5$
$implies s-a=1.5, s-b=0.5 and s-c=0.5$

$implies Area=sqrt(2.5*1.5*0.5*0.5)=sqrt0.9375=0.9682458366$ square units

$implies Area=0.9682458366$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 1 1 , 2 2 , and 2 2 ?