Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 9 units in length?

Answer 1

`9.56 \ 2 \ dp`

Explanation:

Heron's Formula tells us that given all three sides of a triangle, `a,b,c`, say, then the area of the triangle is given by:

`A = sqrt(s(s-a)(s-b)(s-c))`, where `s=1/2(a+b+c)`

So, for the given triangle we have:

`s=1/2(6+4+9) = 19/2`

And so we get:

`A = sqrt(19/2(19/2-6)(19/2-4)(19/2-9))`
`\ \ \ = sqrt(19/2(7/2)(11/2)(1/2))`
`\ \ \ = sqrt(1463/16)`
`\ \ \ = sqrt(1463)/4`
`\ \ \ = 9.562295 ...`
`\ \ \ = 9.56 \ 2 \ dp`