# Area of a Segment of a Circle Formula

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. Formulas to calculate the area of a segment of a circle is given below. According to the definition, the part of circular region which is enclosed between a chord and corresponding arc is known as segment of a circle. The segment portraying a larger area is known as the major segment and the segment having smaller area is known as a **minor** segment.

## Formula of area of a segment

### Solved Examples

**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,

**$\theta$ = 75**

radius = r = 5 inches

**$Area_{radians}$ = $\frac{1}{2}$$r^{2}$($\theta$ – sin$\theta$)**

= $\frac{1}{2}$ $\times$ $5^{2}$ $\times$ (75 – sin75)

= $\frac{1}{2}$ $\times$ 25 $\times$ {75 – (-0.3877)}

= $\frac{1}{2}$ $\times$ 25 $\times$ (75 + 0.3877)

= $\frac{1}{2}$ $\times$ 25 $\times$ (75.3877)

= $\frac{1}{2}$ $\times$ 1884.6925

= 942.34

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