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
212π\dfrac{ 2}{ 12} \pi
.

Correct result:

l =  5.8
S1 =  31.7
S2 =  1.4

Solution:

l=212π11=5.8l = \dfrac{ 2}{ 12} \pi \cdot 11 = 5.8
S1=2212π112=31.7S_1 = \dfrac{ 2}{ 2 \cdot 12} \pi \cdot 11^2 = 31.7
S2=12112(212πsin212π)=1.4S_2 = \dfrac{ 1}{ 2 } \cdot 11^2 ( \dfrac{ 2}{ 12} \pi - \sin \dfrac{ 2}{ 12} \pi ) = 1.4



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