Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `11`, `14`, and `18`?

Answer 1

`Area=76.98` square units

Explanation:

Hero'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=11, b=14` and `c=18`

`implies s=(11+14+18)/2=43/2=21.5`

`implies s=21.5`

`implies s-a=21.5-11=10.5, s-b=21.5-14=7.5 and s-c=21.5-18=3.5`
`implies s-a=10.5, s-b=7.5 and s-c=3.5`

`implies Area=sqrt(21.5*10.5*7.5*3.5)=sqrt5925.9375=76.98` square units

`implies Area=76.98` square units