FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Area of Cyclic Quadrilateral given Circumradius and Angles Formula

GoArea of Cyclic Quadrilateral given Perimeter Formula

GoArea of Cyclic Quadrilateral given Semiperimeter Formula

Fx Copy

LaTeX Copy

Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral. Check FAQs

A = 2 \cdot {(r c)}^{2} \cdot \sin (∠A) \cdot \sin (∠B) \cdot \sin (∠ Diagonals)

A - Area of Cyclic Quadrilateral?r_c - Circumradius of Cyclic Quadrilateral?∠A - Angle A of Cyclic Quadrilateral?∠B - Angle B of Cyclic Quadrilateral?∠_Diagonals - Angle Between Diagonals of Cyclic Quadrilateral?

Area of Cyclic Quadrilateral given Circumradius and Angles Example

With values

With units

Only example

Here is how the Area of Cyclic Quadrilateral given Circumradius and Angles equation looks like with Values.

Here is how the Area of Cyclic Quadrilateral given Circumradius and Angles equation looks like with Units.

Here is how the Area of Cyclic Quadrilateral given Circumradius and Angles equation looks like.

65.1038 = 2 \cdot {(6)}^{2} \cdot \sin (95) \cdot \sin (70) \cdot \sin (105)

65.1038m² = 2 \cdot {(6m)}^{2} \cdot \sin (95°) \cdot \sin (70°) \cdot \sin (105°)

65.1038 = 2 \cdot {(6)}^{2} \cdot \sin (95) \cdot \sin (70) \cdot \sin (105)

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

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

Area of Cyclic Quadrilateral given Circumradius and Angles Solution

Follow our step by step solution on how to calculate Area of Cyclic Quadrilateral given Circumradius and Angles?

FIRST Step Consider the formula

A = 2 \cdot {(r c)}^{2} \cdot \sin (∠A) \cdot \sin (∠B) \cdot \sin (∠ Diagonals)

Next Step Substitute values of Variables

∴

A = 2 \cdot {(6m)}^{2} \cdot \sin (95°) \cdot \sin (70°) \cdot \sin (105°)

Next Step Convert Units

∴

A = 2 \cdot {(6m)}^{2} \cdot \sin (1.6581rad) \cdot \sin (1.2217rad) \cdot \sin (1.8326rad)

Next Step Prepare to Evaluate

∴

A = 2 \cdot {(6)}^{2} \cdot \sin (1.6581) \cdot \sin (1.2217) \cdot \sin (1.8326)

Next Step Evaluate

∴

A = 65.1037967984836m²

LAST Step Rounding Answer

∴

A = 65.1038m²

Area of Cyclic Quadrilateral given Circumradius and Angles Formula Elements

Variables

Functions

Area of Cyclic Quadrilateral

Area of Cyclic Quadrilateral is the amount of 2-dimensional space occupied by the Cyclic Quadrilateral.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Cyclic Quadrilateral

Circumradius of Cyclic Quadrilateral

Circumradius of Cyclic Quadrilateral is the radius of the circumcircle of the Cyclic Quadrilateral.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Cyclic Quadrilateral

Angle A of Cyclic Quadrilateral

Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A.

Symbol: ∠A

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle A of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral is the space between the adjacent sides of Cyclic Quadrilateral, forming angle B.

Symbol: ∠B

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle B of Cyclic Quadrilateral

Angle Between Diagonals of Cyclic Quadrilateral

Angle Between Diagonals of Cyclic Quadrilateral is the measure of the angle formed between the diagonals of the Cyclic Quadrilateral.

Symbol: ∠_Diagonals

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Between Diagonals of Cyclic Quadrilateral

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 Cyclic Quadrilateral

Go Area of Cyclic Quadrilateral given Perimeter

A = \sqrt{(\frac{P}{2} - S a) \cdot (\frac{P}{2} - S b) \cdot (\frac{P}{2} - S c) \cdot (\frac{P}{2} - S d)}

Go Area of Cyclic Quadrilateral given Semiperimeter

A = \sqrt{(s - S a) \cdot (s - S b) \cdot (s - S c) \cdot (s - S d)}

Go Area of Cyclic Quadrilateral given Circumradius

A = \frac{\sqrt{((S a \cdot S b) + (S c \cdot S d)) \cdot ((S a \cdot S c) + (S b \cdot S d)) \cdot ((S a \cdot S d) + (S c \cdot S b))}}{4 \cdot r c}

Go Area of Cyclic Quadrilateral given Angle A

A = \frac{1}{2} \cdot ((S a \cdot S d) + (S b \cdot S c)) \cdot \sin (∠A)

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

Area of Cyclic Quadrilateral given Circumradius and Angles evaluator 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 evaluate 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 evaluate Area of Cyclic Quadrilateral given Circumradius and Angles using this online evaluator? To use this online evaluator 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.

FAQs on Area of Cyclic Quadrilateral given Circumradius and Angles

What is the formula to find Area of Cyclic Quadrilateral given Circumradius and Angles?

The formula of Area of Cyclic Quadrilateral given Circumradius and Angles is expressed as 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). Here is an example- 65.1038 = 2*(6)^2*sin(1.6580627893943)*sin(1.2217304763958)*sin(1.8325957145937).

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

With 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) we can find Area of Cyclic Quadrilateral given Circumradius and Angles using the formula - 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). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Area of Cyclic Quadrilateral?

Here are the different ways to Calculate Area of Cyclic Quadrilateral-

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)

Can the Area of Cyclic Quadrilateral given Circumradius and Angles be negative?

No, the Area of Cyclic Quadrilateral given Circumradius and Angles, measured in Area cannot be negative.

Which unit is used to measure Area of Cyclic Quadrilateral given Circumradius and Angles?

Area of Cyclic Quadrilateral given Circumradius and Angles 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 Cyclic Quadrilateral given Circumradius and Angles can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Area of Cyclic Quadrilateral given Circumradius and Angles Formula

​GoArea of Cyclic Quadrilateral given Perimeter Formula

​GoArea of Cyclic Quadrilateral given Semiperimeter Formula

Area of Cyclic Quadrilateral given Circumradius and Angles Example

Area of Cyclic Quadrilateral given Circumradius and Angles Solution

Area of Cyclic Quadrilateral given Circumradius and Angles Formula Elements

Other Formulas to find Area of Cyclic Quadrilateral

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

FAQs on Area of Cyclic Quadrilateral given Circumradius and Angles

Variable Name

GoArea of Cyclic Quadrilateral given Perimeter Formula

GoArea of Cyclic Quadrilateral given Semiperimeter Formula