Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `12`, `8`, and `11`?

Answer 1

`Area=42.7894` 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=12, b=8` and `c=11`

`implies s=(12+8+11)/2=31/2=15.5`

`implies s=15.5`

`implies s-a=15.5-12=3.5, s-b=15.5-8=7.5 and s-c=15.5-11=4.5`
`implies s-a=3.5, s-b=7.5 and s-c=4.5`

`implies Area=sqrt(15.5*3.5*7.5*4.5)=sqrt1830.9375=42.7894` square units

`implies Area=42.7894` square units