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Area of Cyclic Quadrilateral given Circumradius Formula

GoArea of Cyclic Quadrilateral given Angle A Formula

GoArea of Cyclic Quadrilateral given Angle B Formula

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

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}

A - Area of Cyclic Quadrilateral?S_a - Side A of Cyclic Quadrilateral?S_b - Side B of Cyclic Quadrilateral?S_c - Side C of Cyclic Quadrilateral?S_d - Side D of Cyclic Quadrilateral?r_c - Circumradius of Cyclic Quadrilateral?

Area of Cyclic Quadrilateral given Circumradius Example

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

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

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

58.6672 = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 6}

58.6672m² = \frac{\sqrt{((10m \cdot 9m) + (8m \cdot 5m)) \cdot ((10m \cdot 8m) + (9m \cdot 5m)) \cdot ((10m \cdot 5m) + (8m \cdot 9m))}}{4 \cdot 6m}

58.6672 = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 6}

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Area of Cyclic Quadrilateral given Circumradius Solution

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

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

A = \frac{\sqrt{((10m \cdot 9m) + (8m \cdot 5m)) \cdot ((10m \cdot 8m) + (9m \cdot 5m)) \cdot ((10m \cdot 5m) + (8m \cdot 9m))}}{4 \cdot 6m}

Next Step Prepare to Evaluate

∴

A = \frac{\sqrt{((10 \cdot 9) + (8 \cdot 5)) \cdot ((10 \cdot 8) + (9 \cdot 5)) \cdot ((10 \cdot 5) + (8 \cdot 9))}}{4 \cdot 6}

Next Step Evaluate

∴

A = 58.667199334703m²

LAST Step Rounding Answer

∴

A = 58.6672m²

Area of Cyclic Quadrilateral given Circumradius 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

Side A of Cyclic Quadrilateral

Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side D 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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Area of Cyclic Quadrilateral

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)

Go Area of Cyclic Quadrilateral given Angle B

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

Go Area of Cyclic Quadrilateral given Angle between Diagonals

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

Go Area of Cyclic Quadrilateral given Semiperimeter

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

How to Evaluate Area of Cyclic Quadrilateral given Circumradius?

Area of Cyclic Quadrilateral given Circumradius evaluator uses 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) to evaluate the Area of Cyclic Quadrilateral, The Area of Cyclic Quadrilateral given Circumradius formula is defined as the 2-dimensional space or region occupied by the Cyclic Quadrilateral, calculated using its circumradius. Area of Cyclic Quadrilateral is denoted by A symbol.

How to evaluate Area of Cyclic Quadrilateral given Circumradius using this online evaluator? To use this online evaluator for Area of Cyclic Quadrilateral given Circumradius, enter Side A of Cyclic Quadrilateral (S_a), Side B of Cyclic Quadrilateral (S_b), Side C of Cyclic Quadrilateral (S_c), Side D of Cyclic Quadrilateral (S_d) & Circumradius of Cyclic Quadrilateral (r_c) and hit the calculate button.

FAQs on Area of Cyclic Quadrilateral given Circumradius

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

The formula of Area of Cyclic Quadrilateral given Circumradius is expressed as 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). Here is an example- 58.6672 = sqrt(((10*9)+(8*5))*((10*8)+(9*5))*((10*5)+(8*9)))/(4*6).

How to calculate Area of Cyclic Quadrilateral given Circumradius?

With Side A of Cyclic Quadrilateral (S_a), Side B of Cyclic Quadrilateral (S_b), Side C of Cyclic Quadrilateral (S_c), Side D of Cyclic Quadrilateral (S_d) & Circumradius of Cyclic Quadrilateral (r_c) we can find Area of Cyclic Quadrilateral given Circumradius using the formula - 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). This formula also uses Square Root (sqrt) 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=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 C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral))*sin(Angle Between Diagonals of Cyclic Quadrilateral)

Can the Area of Cyclic Quadrilateral given Circumradius be negative?

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

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

Area of Cyclic Quadrilateral given Circumradius 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 can be measured.

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Area of Cyclic Quadrilateral given Circumradius Formula

​GoArea of Cyclic Quadrilateral given Angle A Formula

​GoArea of Cyclic Quadrilateral given Angle B Formula

Area of Cyclic Quadrilateral given Circumradius Example

Area of Cyclic Quadrilateral given Circumradius Solution

Area of Cyclic Quadrilateral given Circumradius Formula Elements

Other Formulas to find Area of Cyclic Quadrilateral

How to Evaluate Area of Cyclic Quadrilateral given Circumradius?

FAQs on Area of Cyclic Quadrilateral given Circumradius

Variable Name

GoArea of Cyclic Quadrilateral given Angle A Formula

GoArea of Cyclic Quadrilateral given Angle B Formula