Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 4, and 9 units in length?

Answer 1

`A=4sqrt(15)`

Explanation:

Heron's formula states the the area of a traiangle `A` can be calculated as
`A = sqrt(p(p-a)(p-b)(p-c))` where `p = (a+b+c)/2` and `a`, `b` and `c` are the three sides of the triangle.

So for this example
`p = (7+4+9)/2 =10`

`A=sqrt(10(10-7)(10-4)(10-9)) = sqrt(10*4*6*1) =sqrt(240)`

`A=sqrt(16*15) = 4sqrt(15)`