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.

enter image source here

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#

Related questions
See all questions in Circle Arcs and Sectors
Impact of this question
2428 views around the world
You can reuse this answer
Creative Commons License