Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `4`, `4`, and `7`?

Answer 1

`Area=6.777` 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=4, b=4` and `c=7`

`implies s=(4+4+7)/2=15/2=7.5`

`implies s=7.5`

`implies s-a=7.5-4=3.5, s-b=7.5-4=3.5 and s-c=7.5-7=0.5`
`implies s-a=3.5, s-b=3.5 and s-c=0.5`

`implies Area=sqrt(7.5*3.5*3.5*0.5)=sqrt45.9375=6.777` square units

`implies Area=6.777` square units