How do you use Heron's formula to find the area of a triangle with sides of lengths $18$ , $7$ , and $19$ ?

Question

1590 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-23T19:07:39

$Area=62.9285$ square units

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 $a=18, b=7$ and $c=19$

$implies s=(18+7+19)/2=44/2=22$

$implies s=22$

$implies s-a=22-18=4, s-b=22-7=15 and s-c=22-19=3$
$implies s-a=4, s-b=15 and s-c=3$

$implies Area=sqrt(22*4*15*3)=sqrt3960=62.9285$ square units

$implies Area=62.9285$ square units

How do you use Heron's formula to find the area of a triangle with sides of lengths 18 18 , 7 7 , and 19 19 ?