Question

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?

Answer 1

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.

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`