Area of Circle given Chord Length Calculator

✖Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle.ⓘ Chord Length of Circle [l_c]			+10% -10%
✖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.ⓘ Central Angle of Circle [∠_Central]			+10% -10%

✖Area of Circle is the amount of two-dimensional space taken up by a Circle.ⓘ Area of Circle given Chord Length [A]

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Area of Circle given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2
A = pi*(l_c/(2*sin(∠_Central/2)))^2
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)

Variables Used

Area of Circle - (Measured in Square Meter) - Area of Circle is the amount of two-dimensional space taken up by a Circle.
Chord Length of Circle - (Measured in Meter) - Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle.
Central Angle of Circle - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Circle: 8 Meter --> 8 Meter No Conversion Required
Central Angle of Circle: 170 Degree --> 2.9670597283898 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = pi*(l_c/(2*sin(∠_Central/2)))^2 --> pi*(8/(2*sin(2.9670597283898/2)))^2

Evaluating ... ...

A = 50.6502278431295

STEP 3: Convert Result to Output's Unit

50.6502278431295 Square Meter --> No Conversion Required

FINAL ANSWER

50.6502278431295 ≈ 50.65023 Square Meter <-- Area of Circle

(Calculation completed in 00.020 seconds)

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Vellore Institute of Technology (VIT), Bhopal

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< Area of Circle Calculators

Area of Circle given Chord Length

LaTeX Go Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2

Area of Circle given Circumference

LaTeX Go Area of Circle = Circumference of Circle^2/(4*pi)

Area of Circle given Diameter

LaTeX Go Area of Circle = pi/4*Diameter of Circle^2

Area of Circle

LaTeX Go Area of Circle = pi*Radius of Circle^2

Area of Circle given Chord Length Formula

LaTeX Go

Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2
A = pi*(l_c/(2*sin(∠_Central/2)))^2

What is a Circle?

A Circle is a basic two dimensional geometric shape which is defined as the collection of all points on a plane which are in a fixed distance from a fixed point. The fixed point is called the center of the Circle and the fixed distance is called the radius of the Circle. When two radii become collinear, that combined length is called the diameter of the Circle. That is, diameter is the length of the line segment inside the Circle which pass through the center and it will be two times the radius.

How to Calculate Area of Circle given Chord Length?

Area of Circle given Chord Length calculator uses Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2 to calculate 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 calculate Area of Circle given Chord Length using this online calculator? To use this online calculator for Area of Circle given Chord Length, enter Chord Length of Circle (l_c) & Central Angle of Circle (∠_Central) and hit the calculate button. Here is how the Area of Circle given Chord Length calculation can be explained with given input values -> 50.65023 = pi*(8/(2*sin(2.9670597283898/2)))^2.

FAQ

What is Area of Circle given Chord Length?

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 and is represented as A = pi*(l_c/(2*sin(∠_Central/2)))^2 or Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2. Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a 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.

How to calculate Area of Circle given Chord Length?

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 is calculated using Area of Circle = pi*(Chord Length of Circle/(2*sin(Central Angle of Circle/2)))^2. To calculate Area of Circle given Chord Length, you need Chord Length of Circle (l_c) & Central Angle of Circle (∠_Central). With our tool, you need to enter the respective value for Chord Length of Circle & Central Angle of Circle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Circle?

In this formula, Area of Circle uses Chord Length of Circle & Central Angle of Circle. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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