first off, you've posted the formula incorrectly. it should be ...

to justify this formula w/o using the mentioned geometrical relationship requires the use of the calculus ...

consider a sector with a very small , and note the area of a small sector is close to the area of a triangle.

remembering the area of a triangle, , the base is the small arclength equal to and the height is equal to ...

a small sector of the large sector has area

suffice it to say that summing all the small sectors that make up the larger sector results in