Question

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

Answer 1

`A=sqrt3approx1.7321`

Explanation:

Heron's formula states that for a triangle with sides `a,b,c` and a semiperimeter `s=(a+b+c)/2`, the area of the triangle is

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

Here, we know that

`s=(2+2+2)/2=3`

which gives an area of

`A=sqrt(3(3-2)(3-2)(3-2))`

`A=sqrt3approx1.7321`

This problem could also be solved by drawing the equilateral triangle and splitting it into two right triangles with base `1` and height `sqrt3`, giving each right triangle area `sqrt3/2` and the whole triangle an area of `sqrt3`.