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Area of Circle given Chord Length Formula

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Area of Circle is the amount of two-dimensional space taken up by a Circle. Check FAQs

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

A - Area of Circle?l_c - Chord Length of Circle?∠_Central - Central Angle of Circle?π - Archimedes' constant?

Area of Circle given Chord Length Example

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

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

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

50.6502 = 3.1416 \cdot {(\frac{8}{2 \cdot \sin (\frac{170}{2})})}^{2}

50.6502m² = 3.1416 \cdot {(\frac{8m}{2 \cdot \sin (\frac{170°}{2})})}^{2}

50.6502 = 3.1416 \cdot {(\frac{8}{2 \cdot \sin (\frac{170}{2})})}^{2}

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Area of Circle given Chord Length Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = π \cdot {(\frac{8m}{2 \cdot \sin (\frac{170°}{2})})}^{2}

Next Step Substitute values of Constants

∴

A = 3.1416 \cdot {(\frac{8m}{2 \cdot \sin (\frac{170°}{2})})}^{2}

Next Step Convert Units

∴

A = 3.1416 \cdot {(\frac{8m}{2 \cdot \sin (\frac{2.9671rad}{2})})}^{2}

Next Step Prepare to Evaluate

∴

A = 3.1416 \cdot {(\frac{8}{2 \cdot \sin (\frac{2.9671}{2})})}^{2}

Next Step Evaluate

∴

A = 50.6502278431295m²

LAST Step Rounding Answer

∴

A = 50.6502m²

Area of Circle given Chord Length Formula Elements

Variables

Constants

Functions

Area of Circle

Area of Circle is the amount of two-dimensional space taken up by a Circle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Circle

Chord Length of Circle

Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Circle

Central Angle of Circle

Central Angle of Circle is an angle whose apex (vertex) is the centre O of a Circle and whose legs (sides) are radii intersecting the circle in two distinct points.

Symbol: ∠_Central

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle of Circle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

Other Formulas to find Area of Circle

Go Area of Circle

A = π \cdot r^{2}

Go Area of Circle given Diameter

A = \frac{π}{4} \cdot D^{2}

Go Area of Circle given Circumference

A = \frac{C^{2}}{4 \cdot π}

How to Evaluate Area of Circle given Chord Length?

Area of Circle given Chord Length evaluator uses Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2 to evaluate the Area of Circle, Area of Circle given Chord Length formula is defined as the amount of 2D space or region enclosed by a Circle inside its perimeter and is calculated using the length of a particular chord and the central angle of that chord of the Circle. Area of Circle is denoted by A symbol.

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

FAQs on Area of Circle given Chord Length

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

The formula of Area of Circle given Chord Length is expressed as Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2. Here is an example- 50.65023 = pi*(8/(2*sin(2.9670597283898/2)))^2.

How to calculate Area of Circle given Chord Length?

With Chord Length of Circle (l_c) & Central Angle of Circle (∠_Central) we can find Area of Circle given Chord Length using the formula - Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2. This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Area of Circle?

Here are the different ways to Calculate Area of Circle-

Area of Circle=pi*Radius of Circle^2
Area of Circle=pi/4*Diameter of Circle^2
Area of Circle=Circumference of Circle^2/(4*pi)

Can the Area of Circle given Chord Length be negative?

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

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

Area of Circle 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 Circle given Chord Length can be measured.

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