Area of combined shapes

Question

Is it really possible to get the area of the shaded part below because i have tried to divide the figure into several parts but my answer comes to 7.85cm².please someone help me solve it.

Answer 1

Connect the center of the bigger circle with the ends of the chord. You will see that the required area is a combination of two sectors of the big circle and a triangle with the sides $2,2,2\sqrt{3}$. Both circular segments are $30$ degree so the combined area is $1/6$ of the big circle. Thus, the area in question is $\large{\frac{4\pi}{6}+\sqrt{3}}=\frac{2\pi}{3}+\sqrt{3}\approx 3.83$

Answer 2

Area of the shaded portion$$={2\pi} - \int_{1}^{2} 2.\sqrt{4-y^2}dy=3.826$$