Enclosed area=Area of triangle-Area of the sectors


Since you know the triangle is equilateral, you also know that each sector has an angle measuring $60^{\circ}$. The area of these sectors is:

$\(3 \cdot \frac{60}{360} \pi r^2 \)$ Formula for Area of the Sectors

$\(\frac{1}{2} \pi(1)^2=\frac{1}{2} \pi \)$ Substitute and simplify

The area of the triangle is next:

height $\(=\frac{\sqrt{3 }}{2} \cdot hypotenuse \)$ Height of a 30-60-90 triangle

\(height $=\frac{\sqrt{3} }{2} \cdot 2=\sqrt{3} \)$ Substitute 2 for the hypotenuse

The base of the triangle is 2 . Therefore the Area of the Triangle is:

$$
\(\frac{1}{2} \text { base } \cdot \text { height }=\frac{1}{2}(2) \cdot \sqrt{3}=\sqrt{3}\)
$$


Plugging these two Area values into your starting formula, you now calculate the enclosed area: $\(\sqrt{3}-\frac{\pi}{2}\)$, which cannot be simplified. The correct answer choice is $\(\mathbf{D}\)$.