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Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals Formula

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Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle. Check FAQs

P = 2 \cdot D c \cdot \sqrt{1 + (2 \cdot \sin (\frac{π - ∠ d(Obtuse)}{2}) \cdot \cos (\frac{π - ∠ d(Obtuse)}{2}))}

P - Perimeter of Rectangle?D_c - Diameter of Circumcircle of Rectangle?∠_d(Obtuse) - Obtuse Angle between Diagonals of Rectangle?π - Archimedes' constant?

Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals Example

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Here is how the Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals equation looks like with Values.

Here is how the Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals equation looks like with Units.

Here is how the Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals equation looks like.

27.8546 = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 110}{2}) \cdot \cos (\frac{3.1416 - 110}{2}))}

27.8546m = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 110°}{2}) \cdot \cos (\frac{3.1416 - 110°}{2}))}

27.8546 = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 110}{2}) \cdot \cos (\frac{3.1416 - 110}{2}))}

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Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals Solution

Follow our step by step solution on how to calculate Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals?

FIRST Step Consider the formula

P = 2 \cdot D c \cdot \sqrt{1 + (2 \cdot \sin (\frac{π - ∠ d(Obtuse)}{2}) \cdot \cos (\frac{π - ∠ d(Obtuse)}{2}))}

Next Step Substitute values of Variables

∴

P = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (\frac{π - 110°}{2}) \cdot \cos (\frac{π - 110°}{2}))}

Next Step Substitute values of Constants

∴

P = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 110°}{2}) \cdot \cos (\frac{3.1416 - 110°}{2}))}

Next Step Convert Units

∴

P = 2 \cdot 10m \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 1.9199rad}{2}) \cdot \cos (\frac{3.1416 - 1.9199rad}{2}))}

Next Step Prepare to Evaluate

∴

P = 2 \cdot 10 \cdot \sqrt{1 + (2 \cdot \sin (\frac{3.1416 - 1.9199}{2}) \cdot \cos (\frac{3.1416 - 1.9199}{2}))}

Next Step Evaluate

∴

P = 27.8545696128016m

LAST Step Rounding Answer

∴

P = 27.8546m

Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals Formula Elements

Variables

Constants

Functions

Perimeter of Rectangle

Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter of Rectangle

Diameter of Circumcircle of Rectangle

Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: D_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Circumcircle of Rectangle

Obtuse Angle between Diagonals of Rectangle

Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

Symbol: ∠_d(Obtuse)

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle between Diagonals of Rectangle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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 Perimeter of Rectangle

Go Perimeter of Rectangle

P = 2 \cdot (l + b)

Go Perimeter of Rectangle given Diagonal and Length

P = 2 \cdot (l + \sqrt{d^{2} - l^{2}})

Go Perimeter of Rectangle given Area and Length

P = \frac{2 \cdot (A + l^{2})}{l}

Go Perimeter of Rectangle given Breadth and Circumradius

P = 2 \cdot (b + \sqrt{(4 \cdot {r c}^{2}) - b^{2}})

How to Evaluate Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals?

Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals evaluator uses Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2))) to evaluate the Perimeter of Rectangle, The Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Diameter of Circumcircle and Obtuse Angle between Diagonals of the Rectangle. Perimeter of Rectangle is denoted by P symbol.

How to evaluate Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals using this online evaluator? To use this online evaluator for Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals, enter Diameter of Circumcircle of Rectangle (D_c) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) and hit the calculate button.

FAQs on Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals

What is the formula to find Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals?

The formula of Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals is expressed as Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2))). Here is an example- 27.85457 = 2*10*sqrt(1+(2*sin((pi-1.9198621771934)/2)*cos((pi-1.9198621771934)/2))).

How to calculate Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals?

With Diameter of Circumcircle of Rectangle (D_c) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) we can find Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals using the formula - Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Perimeter of Rectangle?

Here are the different ways to Calculate Perimeter of Rectangle-

Perimeter of Rectangle=2*(Length of Rectangle+Breadth of Rectangle)
Perimeter of Rectangle=2*(Length of Rectangle+sqrt(Diagonal of Rectangle^2-Length of Rectangle^2))
Perimeter of Rectangle=(2*(Area of Rectangle+Length of Rectangle^2))/Length of Rectangle

Can the Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals be negative?

No, the Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals, measured in Length cannot be negative.

Which unit is used to measure Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals?

Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Perimeter of Rectangle given Diameter of Circumcircle and Obtuse Angle between Diagonals can be measured.

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