The triangle can be divided into 3 congruent triangle by drawing lines from the center to the vertices. (Sorry if my diagram does not appear to have congruent sub-triangles; they really are congruent).
![enter image source here]()
Each of these 3 sub-triangles can be divided into 2 sub-sub-triangles with a 60^circ, a right angle, and a hypotenuse of length 4
The 60^circ right-angled triangle is one of the standard triangles
and given a hypotenuse of 4
the other two sides will have lengths 2 and 2sqrt(3) as indicated above.
The Area of each of these sub-sub-triangles will be
color(white)("XXX")A_"sst"=(2xx2sqrt(3))/2 = 2sqrt(3)
Since the original triangle is composed of 6 such sub-sub-triangles
the area of the original triangle must be
color(white)("XXX")6xx2sqrt(3)=12sqrt(3)
