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Area of sector is the part of the circle enclosed by an arc and two radii drawn to the extremities. Area of a sector can be calculated using the radius(r) and the angle(θ) created by the two radii at the center of the circle. Area of the sector is represented in length – unit2unit2 irrespective of whether the angle given is in degrees or radians. A sector with the central angle of 180° is called a half-disk and is bounded by a diameter and a semicircle. Sectors with other central angles are sometimes given special names, these include quadrants (90°), sextants (60°) and octants (45°), which come from the sector being one 4th or 6th or 8th part of a full circle.

The **Area of a Sector Formula** is, A = πr2r2(θ360θ360)

Where,

r is the radius of the circle.

θ is the angle created by the two radii at the center of the circle.

### SOLVED EXAMPLES

**Question 1: Find the area of a sector of a circle whose radius is 8 cm and the angle made at the center of the circle is 45**^{o}
**Solution:**

Given,

r = 8 cm

θθ = 45^{o
}Area of a sector

= πr^{2 }(θ360θ360)

= π ×× 8^{2 ××} (4536045360) cm^{2
}= π ×× 64 ×× 0.125 cm^{2
}= 25.12 cm^{2}