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Area of a Segment of a Circle Formula
| Formula To Calculate Area of a Segment of a Circle | |
|---|---|
| Area of a Segment in Radians | A = (½) × r2 (θ – Sin θ) |
| Area of a Segment in Degrees | A = (½) × r 2 × [(π/180) θ – sin θ] |
- How do you find the area of a chord of a circle?
- What is the formula of chord?
- What is the formula for finding the area of an arc?
- What is the formula for area of a sector?
How do you find the area of a chord of a circle?
The area of the segment of the circle (or) minor segment of a circle is:
- (θ / 360o) × πr2 - (1/2) r2 sin θ (OR) r2 [πθ/360o - sin θ/2], if 'θ' is in degrees.
- (1/2) × r2θ - (1/2) r2 sin θ (OR) (r2 / 2) [θ - sin θ], if 'θ' is in radians.
What is the formula of chord?
The chord of a circle can be stated as a line segment joining two points on the circumference of the circle.
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How to Find the Length of the Chord?
| Chord Length Formula Using Perpendicular Distance from the Centre | Chord Length = 2 × √(r² - d²) |
|---|---|
| Chord Length Formula Using Trigonometry | Chord Length = 2 × r × sin(c/2) |
What is the formula for finding the area of an arc?
Explanation: If the central angle measures 60 degrees, divide the 360 total degrees in the circle by 60. Multiply this by the measure of the corresponding arc to find the total circumference of the circle. Use the circumference to find the radius, then use the radius to find the area.
What is the formula for area of a sector?
The formula for the area of the sector is θ360∘×πr2 θ 360 ∘ × π r 2 .
