A circular **segment** is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord. In other words, it is two equal halves that are divided by the **circle’s arc** and connected through chord by the endpoints of the arc. The **formulas to calculate the area of a segment of a circle** is given below. According to the definition, the part of the circular region which is enclosed between a chord and corresponding arc is known as the segment of a circle. The segment portraying a larger area is known as the major segment and the segment having a smaller area is known as a **minor** segment.

Formula To Calculate Area of a Segment of a Circle | |
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Area of a Segment in Radians | A = (1⁄2) × r^{2} (θ – Sin θ) |

Area of a Segment in Degrees | A = (½) × r ^{2 } × [(π/180) θ – sin θ] |

### Solved Example Question

**Question 1: ** Find the area of a segment of a circle with a central angle of 75 degrees and a radius of 5 inches.

** Solution: **

Given,

θ = 75

radius = r = 5 inches

Area_{radians} = 12 r^{2} (θ – sin θ)

= 12 × 52 × (75 – sin75)

= 12 × 25 × 75 –(− 0.3877)

= 12 × 25 × (75 + 0.3877)

= 12 × 25 × (75.3877)

= 12 × 1884.6925

= 942.34