Find the area of the segment of the circle of radius whose corresponding sector has a central angle of . ( use )
Solve for area of the given segment
Given,
From the figure we can say that,
Area of segment Area of sector Area of
Step 1: Find area of
According to the figure,
Hence, forms equilateral triangle of side
Area of
Area of
Step 2: Find area of sector
According to the figure, radius of the circle and
central angle formed by sector
We know that, area of sector
Area of sector
Area of sector
Step 3: Find area of segment
Area of segment Area of sector Area of
Area of the segment
Hence, area of segment is