https://cracku.in/cat/history/1689698?src=test. Pls elaborate on the solution of Q5

Question:
A closed barn ABCD in the shape of a Rhombus is situated inside a vast field. Each side of the barn is equal to 10m and angle A = 60 degrees. A cow is tied to point A outside the barn with a rope of length 20m. Find the area of the field that the cow can graze.

Solution:
The cow can graze the whole area of a circle of radius 20m if the barn wasn't there. Because the barn is there it can graze 300 degrees angle out of 360 degrees because 60 degrees is cut by the barn at the vertex A. This means it can graze $$\frac{5}{6}$$th of the area of the circle of radius 20m.
This area = $$\frac{5}{6}\times\pi\times20^2=\frac{1000\pi}{3}$$.

It can also graze two sectors of circles centered at B and D of radius 10m and angle 60 degrees.
This area = $$2\times(\frac{1}{6}\times\pi\times10^2)=\frac{100\pi}{3}$$

Total area = $$\frac{1000\pi}{3}+\frac{100\pi}{3}=\frac{1100\pi}{3}$$