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Area of Circular Segment given Chord Length Formula

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Area of Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment. Check FAQs

A = \frac{(2 \cdot ∠ Central) - \sin (∠ Central)}{4} \cdot \frac{{l c}^{2}}{2 - (2 \cdot \cos (∠ Central))}

A - Area of Circular Segment?∠_Central - Central Angle of Circular Segment?l_c - Chord Length of Circular Segment?

Area of Circular Segment given Chord Length Example

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Here is how the Area of Circular Segment given Chord Length equation looks like with Values.

Here is how the Area of Circular Segment given Chord Length equation looks like with Units.

Here is how the Area of Circular Segment given Chord Length equation looks like.

39.2699 = \frac{(2 \cdot 180) - \sin (180)}{4} \cdot \frac{10^{2}}{2 - (2 \cdot \cos (180))}

39.2699m² = \frac{(2 \cdot 180°) - \sin (180°)}{4} \cdot \frac{{10m}^{2}}{2 - (2 \cdot \cos (180°))}

39.2699 = \frac{(2 \cdot 180) - \sin (180)}{4} \cdot \frac{10^{2}}{2 - (2 \cdot \cos (180))}

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Area of Circular Segment given Chord Length Solution

Follow our step by step solution on how to calculate Area of Circular Segment given Chord Length?

FIRST Step Consider the formula

A = \frac{(2 \cdot ∠ Central) - \sin (∠ Central)}{4} \cdot \frac{{l c}^{2}}{2 - (2 \cdot \cos (∠ Central))}

Next Step Substitute values of Variables

∴

A = \frac{(2 \cdot 180°) - \sin (180°)}{4} \cdot \frac{{10m}^{2}}{2 - (2 \cdot \cos (180°))}

Next Step Convert Units

∴

A = \frac{(2 \cdot 3.1416rad) - \sin (3.1416rad)}{4} \cdot \frac{{10m}^{2}}{2 - (2 \cdot \cos (3.1416rad))}

Next Step Prepare to Evaluate

∴

A = \frac{(2 \cdot 3.1416) - \sin (3.1416)}{4} \cdot \frac{10^{2}}{2 - (2 \cdot \cos (3.1416))}

Next Step Evaluate

∴

A = 39.2699081698613m²

LAST Step Rounding Answer

∴

A = 39.2699m²

Area of Circular Segment given Chord Length Formula Elements

Variables

Functions

Area of Circular Segment

Area of Circular Segment is the total quantity of plane enclosed by the boundary of a Circular Segment.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Circular Segment

Central Angle of Circular Segment

Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.

Symbol: ∠_Central

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle of Circular Segment

Chord Length of Circular Segment

Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Circular Segment

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Area of Circular Segment

Go Area of Circular Segment

A = \frac{(2 \cdot ∠ Central) - \sin (∠ Central)}{4} \cdot r^{2}

How to Evaluate Area of Circular Segment given Chord Length?

Area of Circular Segment given Chord Length evaluator uses Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))) to evaluate the Area of Circular Segment, Area of Circular Segment given Chord Length formula is defined as the amount of 2D space bounded by a chord and a corresponding arc and calculated using the chord length of the Circular Segment. Area of Circular Segment is denoted by A symbol.

How to evaluate Area of Circular Segment given Chord Length using this online evaluator? To use this online evaluator for Area of Circular Segment given Chord Length, enter Central Angle of Circular Segment (∠_Central) & Chord Length of Circular Segment (l_c) and hit the calculate button.

FAQs on Area of Circular Segment given Chord Length

What is the formula to find Area of Circular Segment given Chord Length?

The formula of Area of Circular Segment given Chord Length is expressed as Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))). Here is an example- 39.26991 = ((2*3.1415926535892)-sin(3.1415926535892))/4*(10^2)/(2-(2*cos(3.1415926535892))).

How to calculate Area of Circular Segment given Chord Length?

With Central Angle of Circular Segment (∠_Central) & Chord Length of Circular Segment (l_c) we can find Area of Circular Segment given Chord Length using the formula - Area of Circular Segment = ((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*(Chord Length of Circular Segment^2)/(2-(2*cos(Central Angle of Circular Segment))). This formula also uses Sine, Cosine function(s).

What are the other ways to Calculate Area of Circular Segment?

Here are the different ways to Calculate Area of Circular Segment-

Area of Circular Segment=((2*Central Angle of Circular Segment)-sin(Central Angle of Circular Segment))/4*Radius of Circular Segment^2

Can the Area of Circular Segment given Chord Length be negative?

No, the Area of Circular Segment given Chord Length, measured in Area cannot be negative.

Which unit is used to measure Area of Circular Segment given Chord Length?

Area of Circular Segment given Chord Length is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Circular Segment given Chord Length can be measured.

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