geometry

Minor arc AB in the diagram is 30 degrees and the radius of the circle is 16. Find the area of circular segment AB.

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\(A=\frac{30}{360}\cdot \pi\cdot r^2-\frac{1}{2}\cdot r\cdot h\)

\(\color{BrickRed}r=16\\ h=r\cdot sin\ {\color{BrickRed}30°}=16\cdot 0.5\\ \color{blue}h=8\)

\(A=\frac{1}{12}\cdot \pi\cdot 16^2-\frac{1}{2}\cdot 16\cdot 8\)

\(A=3.021\)

  !

Area of entire sector - triangle = shaded area

30 / 360 * pi r^2  - 1/2 ab sin30

30/360 * pi * 16² - 1/2 (16)(16) sin30 = 3.0206  units²