Since the radius has length 4, and the triangle has sides of length 4, we can see we have the following equilateral triangle in our diagram:



Since we have an equilateral triangle, each angle inside the triangle must be 60° as follows:



Now we'll find the area of the green sector below:

Area of sector $=(\frac{60}{360})(\pi)(4^2)$
$=(\frac{1}{6})(\pi)(16)$


Now we'll find the area of the red equilateral triangle below

We'll use the formula for the area of an equilateral triangle: Area $= (\frac{\sqrt{3}}{4})(side^2)$
$= (\frac{\sqrt{3}}{4})(4^2)$
$= (\frac{\sqrt{3}}{4})(16)$
$= 4\sqrt{3}$

The area of the shaded region = (area of green sector) - (area of red equilateral triangle)
$=(\frac{1}{6})(\pi)(16)-4\sqrt{3}$
$≈1.45$

A is closest.

Answer: A