Arc and segment

Calculate the length of circular arc l, area of the circular arc S₁ and area of circular segment S₂. Radius of the circle is 11 and corresponding angle is

${\displaystyle \frac{2}{12}}\pi$

.

Correct result:

l =  5.8
S₁ =  31.7
S₂ =  1.4

Solution:

$l={\displaystyle \frac{2}{12}}\pi \cdot 11=5.8$

$S_1={\displaystyle \frac{2}{2\cdot 12}}\pi \cdot 11^2=31.7$

$S_2={\displaystyle \frac{1}{2}}\cdot 11^2({\displaystyle \frac{2}{12}}\pi -\sin {\displaystyle \frac{2}{12}}\pi )=1.4$

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