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Find the area of the shaded region in the figure:
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
The area of a circular segment is the difference of the area of circular sector and a triangle.
The area of a circular sector is given by the formula
Substitute the values of r and θ, we have
Since the unit of area is square units, then the unit of an angle must be in radians since it is a unit less value of angle. Let's convert the unit of an angle in radians as follows
The area of a triangle given the two sides and the adjacent angle is given by the formula
Since the triangle is inscribed in a circle whose vertex is a center of a circle, then it follows that a = b = r. The above equation becomes
Substitute the values of r and θ, we have
Therefore, the area of circular segment is
