Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `9`, `4`, and `8`?

Answer 1

`Area=15.998` 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=9, b=4` and `c=8`

`implies s=(9+4+8)/2=21/2=10.5`

`implies s=10.5`

`implies s-a=10.5-9=1.5, s-b=10.5-4=6.5 and s-c=10.5-8=2.5`
`implies s-a=1.5, s-b=6.5 and s-c=2.5`

`implies Area=sqrt(10.5*1.5*6.5*2.5)=sqrt255.9375=15.998` square units

`implies Area=15.998` square units