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Area of Cyclic Quadrilateral given Angle C Formula

GoArea of Cyclic Quadrilateral given Perimeter Formula

GoArea of Cyclic Quadrilateral given Semiperimeter 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{1}{2} \cdot ((S a \cdot S d) + (S b \cdot S c)) \cdot \sin (∠C)

A - Area of Cyclic Quadrilateral?S_a - Side A of Cyclic Quadrilateral?S_d - Side D of Cyclic Quadrilateral?S_b - Side B of Cyclic Quadrilateral?S_c - Side C of Cyclic Quadrilateral?∠C - Angle C of Cyclic Quadrilateral?

Area of Cyclic Quadrilateral given Angle C Example

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

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

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

60.7679 = \frac{1}{2} \cdot ((10 \cdot 5) + (9 \cdot 8)) \cdot \sin (85)

60.7679m² = \frac{1}{2} \cdot ((10m \cdot 5m) + (9m \cdot 8m)) \cdot \sin (85°)

60.7679 = \frac{1}{2} \cdot ((10 \cdot 5) + (9 \cdot 8)) \cdot \sin (85)

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Area of Cyclic Quadrilateral given Angle C Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{1}{2} \cdot ((10m \cdot 5m) + (9m \cdot 8m)) \cdot \sin (85°)

Next Step Convert Units

∴

A = \frac{1}{2} \cdot ((10m \cdot 5m) + (9m \cdot 8m)) \cdot \sin (1.4835rad)

Next Step Prepare to Evaluate

∴

A = \frac{1}{2} \cdot ((10 \cdot 5) + (9 \cdot 8)) \cdot \sin (1.4835)

Next Step Evaluate

∴

A = 60.767876583595m²

LAST Step Rounding Answer

∴

A = 60.7679m²

Area of Cyclic Quadrilateral given Angle C 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 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

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

Angle C of Cyclic Quadrilateral

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

Symbol: ∠C

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle C 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 Circumradius and Angles

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

How to Evaluate Area of Cyclic Quadrilateral given Angle C?

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

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

FAQs on Area of Cyclic Quadrilateral given Angle C

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

The formula of Area of Cyclic Quadrilateral given Angle C is expressed as 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). Here is an example- 60.76788 = 1/2*((10*5)+(9*8))*sin(1.4835298641949).

How to calculate Area of Cyclic Quadrilateral given Angle C?

With Side A of Cyclic Quadrilateral (S_a), Side D of Cyclic Quadrilateral (S_d), Side B of Cyclic Quadrilateral (S_b), Side C of Cyclic Quadrilateral (S_c) & Angle C of Cyclic Quadrilateral (∠C) we can find Area of Cyclic Quadrilateral given Angle C using the formula - 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). 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 Angle C be negative?

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

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

Area of Cyclic Quadrilateral given Angle C 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 Angle C can be measured.

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Area of Cyclic Quadrilateral given Angle C Formula

​GoArea of Cyclic Quadrilateral given Perimeter Formula

​GoArea of Cyclic Quadrilateral given Semiperimeter Formula

Area of Cyclic Quadrilateral given Angle C Example

Area of Cyclic Quadrilateral given Angle C Solution

Area of Cyclic Quadrilateral given Angle C Formula Elements

Other Formulas to find Area of Cyclic Quadrilateral

How to Evaluate Area of Cyclic Quadrilateral given Angle C?

FAQs on Area of Cyclic Quadrilateral given Angle C

Variable Name

GoArea of Cyclic Quadrilateral given Perimeter Formula

GoArea of Cyclic Quadrilateral given Semiperimeter Formula