Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `1`, `5`, and `5`?

Answer 1

`Area=2.48746` square units

Explanation:

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=5` and `c=5`

`implies s=(1+5+5)/2=11/2=5.5`

`implies s=5.5`

`implies s-a=5.5-1=4.5, s-b=5.5-5=0.5 and s-c=5.5-5=0.5`
`implies s-a=4.5, s-b=0.5 and s-c=0.5`

`implies Area=sqrt(5.5*4.5*0.5*0.5)=sqrt6.1875=2.48746` square units

`implies Area=2.48746` square units