Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `2`, `7`, and `7`?

Answer 1

`4sqrt3`

Explanation:

In order to use Heron's formula, we will have to know the semiperimeter of the triangle. The semiperimeter is simply one half the perimeter of the triangle, so the semiperimeter `s` of a triangle with sides `a,b,c` can be expressed as

`s=(a+b+c)/2`

Thus, our current semiperimeter is

`s=(2+7+7)/2=8`

Now, we can apply Heron's formula, which states that the area `A` of a triangle can be found through

`A=sqrt(s(s-a)(s-b)(s-c))`

We know that `s=8,a=2,b=7,c=7`, so

`A=sqrt(8(8-2)(8-7)(8-7))`

`A=sqrt48`

`A=4sqrt3`