the area of the sector with
radians and
square units.
The formula for the area (A) of a sector of a circle is given by:
![\[ A = (1)/(2)r^2\theta \]](https://img.qammunity.org/2024/formulas/mathematics/college/twhnfgqx7zoughcwjn0btlpp8bc6hq0nsb.png)
where:
- r is the radius of the circle,
-
is the central angle of the sector in radians.
Given r = 2 and
, substitute these values into the formula:
![\[ A = (1)/(2) \cdot (2)^2 \cdot (\pi)/(9) \]](https://img.qammunity.org/2024/formulas/mathematics/college/4vo4pj3rzdeujjerbi8m7el0nxtyyr75dx.png)
Simplify:
![\[ A = (1)/(2) \cdot 4 \cdot (\pi)/(9) \]](https://img.qammunity.org/2024/formulas/mathematics/college/k1n8b8lgtbkqxtzwl5irakbbnjin4uy8qt.png)
![\[ A = (2\pi)/(9) \]](https://img.qammunity.org/2024/formulas/mathematics/college/hofv2u6lhxgdieqgx08nz766p0pdexbevg.png)
So, the area of the sector with
radians and r = 2 is
square units.