Area of Cyclic Quadrilateral given Circumradius and Angles Calculator

✖Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.ⓘ Circumradius of Cyclic Quadrilateral [r_c]			+10% -10%
✖Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A.ⓘ Angle A of Cyclic Quadrilateral [∠A]			+10% -10%
✖Angle B of Cyclic Quadrilateral is the space between the adjacent sides of Cyclic Quadrilateral, forming angle B.ⓘ Angle B of Cyclic Quadrilateral [∠B]			+10% -10%
✖Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.ⓘ Angle Between Diagonals of Cyclic Quadrilateral [∠_Diagonals]			+10% -10%

✖Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.ⓘ Area of Cyclic Quadrilateral given Circumradius and Angles [A]

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Area of Cyclic Quadrilateral given Circumradius and Angles

Formula

`"A" = 2*("r"_{"c"})^2*sin("∠A")*sin("∠B")*sin("∠"_{"Diagonals"})`

Example

`"65.1038m²"=2*("6m")^2*sin("95°")*sin("70°")*sin("105°")`

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Area of Cyclic Quadrilateral given Circumradius and Angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Cyclic Quadrilateral = 2*(Circumradius of Cyclic Quadrilateral)^2*sin(Angle A of Cyclic Quadrilateral)*sin(Angle B of Cyclic Quadrilateral)*sin(Angle Between Diagonals of Cyclic Quadrilateral)
A = 2*(r_c)^2*sin(∠A)*sin(∠B)*sin(∠_Diagonals)
This formula uses 1 Functions, 5 Variables

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 Cyclic Quadrilateral - (Measured in Square Meter) - Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.
Circumradius of Cyclic Quadrilateral - (Measured in Meter) - Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.
Angle A of Cyclic Quadrilateral - (Measured in Radian) - Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A.
Angle B of Cyclic Quadrilateral - (Measured in Radian) - Angle B of Cyclic Quadrilateral is the space between the adjacent sides of Cyclic Quadrilateral, forming angle B.
Angle Between Diagonals of Cyclic Quadrilateral - (Measured in Radian) - Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Cyclic Quadrilateral: 6 Meter --> 6 Meter No Conversion Required
Angle A of Cyclic Quadrilateral: 95 Degree --> 1.6580627893943 Radian (Check conversion here)
Angle B of Cyclic Quadrilateral: 70 Degree --> 1.2217304763958 Radian (Check conversion here)
Angle Between Diagonals of Cyclic Quadrilateral: 105 Degree --> 1.8325957145937 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 2*(r_c)^2*sin(∠A)*sin(∠B)*sin(∠_Diagonals) --> 2*(6)^2*sin(1.6580627893943)*sin(1.2217304763958)*sin(1.8325957145937)

Evaluating ... ...

A = 65.1037967984836

STEP 3: Convert Result to Output's Unit

65.1037967984836 Square Meter --> No Conversion Required

FINAL ANSWER

65.1037967984836 ≈ 65.1038 Square Meter <-- Area of Cyclic Quadrilateral

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Cyclic Quadrilateral » Area of Cyclic Quadrilateral » Area of Cyclic Quadrilateral given Circumradius and Angles

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< 9 Area of Cyclic Quadrilateral Calculators

Area of Cyclic Quadrilateral given Circumradius

Go Area of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Circumradius of Cyclic Quadrilateral)

Area of Cyclic Quadrilateral given Semiperimeter

Go Area of Cyclic Quadrilateral = sqrt((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))

Area of Cyclic Quadrilateral given Perimeter

Go Area of Cyclic Quadrilateral = sqrt((Perimeter of Cyclic Quadrilateral/2-Side A of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side B of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side C of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side D of Cyclic Quadrilateral))

Area of Cyclic Quadrilateral given Circumradius and Angles

Go Area of Cyclic Quadrilateral = 2*(Circumradius of Cyclic Quadrilateral)^2*sin(Angle A of Cyclic Quadrilateral)*sin(Angle B of Cyclic Quadrilateral)*sin(Angle Between Diagonals of Cyclic Quadrilateral)

Area of Cyclic Quadrilateral given Angle between Diagonals

Go Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle Between Diagonals of Cyclic Quadrilateral)

Area of Cyclic Quadrilateral given Angle A

Go Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))*sin(Angle A of Cyclic Quadrilateral)

Area of Cyclic Quadrilateral given Angle B

Go Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle B of Cyclic Quadrilateral)

Area of Cyclic Quadrilateral given Angle D

Area of Cyclic Quadrilateral given Angle C

Area of Cyclic Quadrilateral given Circumradius and Angles Formula

What is a Cyclic Quadrilateral?

A Cyclic Quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that there exists a circle that passes through all four vertices of the quadrilateral. Cyclic quadrilaterals are useful in various types of geometry problems, particularly those in which angle chasing is required.

How to Calculate Area of Cyclic Quadrilateral given Circumradius and Angles?

Area of Cyclic Quadrilateral given Circumradius and Angles calculator uses Area of Cyclic Quadrilateral = 2*(Circumradius of Cyclic Quadrilateral)^2*sin(Angle A of Cyclic Quadrilateral)*sin(Angle B of Cyclic Quadrilateral)*sin(Angle Between Diagonals of Cyclic Quadrilateral) to calculate the Area of Cyclic Quadrilateral, The Area of Cyclic Quadrilateral given Circumradius and Angles formula is defined as the 2-dimensional space or region occupied by the Cyclic Quadrilateral, calculated using its circumradius and angles. Area of Cyclic Quadrilateral is denoted by A symbol.

How to calculate Area of Cyclic Quadrilateral given Circumradius and Angles using this online calculator? To use this online calculator for Area of Cyclic Quadrilateral given Circumradius and Angles, enter Circumradius of Cyclic Quadrilateral (r_c), Angle A of Cyclic Quadrilateral (∠A), Angle B of Cyclic Quadrilateral (∠B) & Angle Between Diagonals of Cyclic Quadrilateral (∠_Diagonals) and hit the calculate button. Here is how the Area of Cyclic Quadrilateral given Circumradius and Angles calculation can be explained with given input values -> 65.1038 = 2*(6)^2*sin(1.6580627893943)*sin(1.2217304763958)*sin(1.8325957145937).

FAQ

What is Area of Cyclic Quadrilateral given Circumradius and Angles?

The Area of Cyclic Quadrilateral given Circumradius and Angles formula is defined as the 2-dimensional space or region occupied by the Cyclic Quadrilateral, calculated using its circumradius and angles and is represented as A = 2*(r_c)^2*sin(∠A)*sin(∠B)*sin(∠_Diagonals) or Area of Cyclic Quadrilateral = 2*(Circumradius of Cyclic Quadrilateral)^2*sin(Angle A of Cyclic Quadrilateral)*sin(Angle B of Cyclic Quadrilateral)*sin(Angle Between Diagonals of Cyclic Quadrilateral). Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral, Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A, Angle B of Cyclic Quadrilateral is the space between the adjacent sides of Cyclic Quadrilateral, forming angle B & Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.

How to calculate Area of Cyclic Quadrilateral given Circumradius and Angles?

The Area of Cyclic Quadrilateral given Circumradius and Angles formula is defined as the 2-dimensional space or region occupied by the Cyclic Quadrilateral, calculated using its circumradius and angles is calculated using Area of Cyclic Quadrilateral = 2*(Circumradius of Cyclic Quadrilateral)^2*sin(Angle A of Cyclic Quadrilateral)*sin(Angle B of Cyclic Quadrilateral)*sin(Angle Between Diagonals of Cyclic Quadrilateral). To calculate Area of Cyclic Quadrilateral given Circumradius and Angles, you need Circumradius of Cyclic Quadrilateral (r_c), Angle A of Cyclic Quadrilateral (∠A), Angle B of Cyclic Quadrilateral (∠B) & Angle Between Diagonals of Cyclic Quadrilateral (∠_Diagonals). With our tool, you need to enter the respective value for Circumradius of Cyclic Quadrilateral, Angle A of Cyclic Quadrilateral, Angle B of Cyclic Quadrilateral & Angle Between Diagonals of Cyclic Quadrilateral 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 Cyclic Quadrilateral?

In this formula, Area of Cyclic Quadrilateral uses Circumradius of Cyclic Quadrilateral, Angle A of Cyclic Quadrilateral, Angle B of Cyclic Quadrilateral & Angle Between Diagonals of Cyclic Quadrilateral. We can use 8 other way(s) to calculate the same, which is/are as follows -

Area of Cyclic Quadrilateral = sqrt((Perimeter of Cyclic Quadrilateral/2-Side A of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side B of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side C of Cyclic Quadrilateral)*(Perimeter of Cyclic Quadrilateral/2-Side D of Cyclic Quadrilateral))
Area of Cyclic Quadrilateral = sqrt((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))
Area of Cyclic Quadrilateral = sqrt(((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)))/(4*Circumradius of Cyclic Quadrilateral)
Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))*sin(Angle A of Cyclic Quadrilateral)
Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle B of Cyclic Quadrilateral)
Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side B of Cyclic Quadrilateral)+(Side C of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle D of Cyclic Quadrilateral)
Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))*sin(Angle C of Cyclic Quadrilateral)
Area of Cyclic Quadrilateral = 1/2*((Side A of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle Between Diagonals of Cyclic Quadrilateral)

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