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)/2πr22

Explanation:

Radian describes an angle subtended by an arc of circle, whose length is equal to its radius. As circumference of a circle is 2pi2π times radius, complete circle is 2pi2π radians and a semicircle subtends an anglre of piπ radians.

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As area of a circle is given by 1/2r^2theta12r2θ, (where thetaθ is in radians)

as semicircle subtendsan angle piπ radians, its area is

1/2r^2xxpi=(pir^2)/212r2×π=πr22

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