How do we express area of a sector of a circle in terms of angle in radians? What is the area of a semicircle using this?

1 Answer
Shwetank Mauria
Sep 27, 2017

Area of semicircle is #(pir^2)/2#

Explanation:

Radian describes an angle subtended by an arc of circle, whose length is equal to its radius. As circumference of a circle is #2pi# times radius, complete circle is #2pi# radians and a semicircle subtends an anglre of #pi# radians.

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As area of a circle is given by #1/2r^2theta#, (where #theta# is in radians)

as semicircle subtendsan angle #pi# radians, its area is

#1/2r^2xxpi=(pir^2)/2#

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