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Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth Formula

GoPerimeter of Rectangle Formula

GoPerimeter of Rectangle given Diagonal and Length Formula

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

P = 4 \cdot r c \cdot \sqrt{1 + (2 \cdot \sin ((\frac{π}{2}) - ∠ db) \cdot \cos ((\frac{π}{2}) - ∠ db))}

P - Perimeter of Rectangle?r_c - Circumradius of Rectangle?∠_db - Angle between Diagonal and Breadth of Rectangle?π - Archimedes' constant?

Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth Example

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Here is how the Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth equation looks like with Values.

Here is how the Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth equation looks like with Units.

Here is how the Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth equation looks like.

27.8546 = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 55) \cdot \cos ((\frac{3.1416}{2}) - 55))}

27.8546m = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 55°) \cdot \cos ((\frac{3.1416}{2}) - 55°))}

27.8546 = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 55) \cdot \cos ((\frac{3.1416}{2}) - 55))}

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Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth Solution

Follow our step by step solution on how to calculate Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth?

FIRST Step Consider the formula

P = 4 \cdot r c \cdot \sqrt{1 + (2 \cdot \sin ((\frac{π}{2}) - ∠ db) \cdot \cos ((\frac{π}{2}) - ∠ db))}

Next Step Substitute values of Variables

∴

P = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin ((\frac{π}{2}) - 55°) \cdot \cos ((\frac{π}{2}) - 55°))}

Next Step Substitute values of Constants

∴

P = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 55°) \cdot \cos ((\frac{3.1416}{2}) - 55°))}

Next Step Convert Units

∴

P = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 0.9599rad) \cdot \cos ((\frac{3.1416}{2}) - 0.9599rad))}

Next Step Prepare to Evaluate

∴

P = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin ((\frac{3.1416}{2}) - 0.9599) \cdot \cos ((\frac{3.1416}{2}) - 0.9599))}

Next Step Evaluate

∴

P = 27.8545696128016m

LAST Step Rounding Answer

∴

P = 27.8546m

Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth 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

Circumradius of Rectangle

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Rectangle

Angle between Diagonal and Breadth of Rectangle

Angle between Diagonal and Breadth of Rectangle is the measure of wideness of the angle made by any diagonal with the breadth of the Rectangle.

Symbol: ∠_db

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle between Diagonal and Breadth 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 Circumradius and Angle between Diagonal and Breadth?

Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth evaluator uses Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin((pi/2)-Angle between Diagonal and Breadth of Rectangle)*cos((pi/2)-Angle between Diagonal and Breadth of Rectangle))) to evaluate the Perimeter of Rectangle, The Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Angle between Diagonal and Breadth of the Rectangle. Perimeter of Rectangle is denoted by P symbol.

How to evaluate Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth using this online evaluator? To use this online evaluator for Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth, enter Circumradius of Rectangle (r_c) & Angle between Diagonal and Breadth of Rectangle (∠_db) and hit the calculate button.

FAQs on Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth

What is the formula to find Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth?

The formula of Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth is expressed as Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin((pi/2)-Angle between Diagonal and Breadth of Rectangle)*cos((pi/2)-Angle between Diagonal and Breadth of Rectangle))). Here is an example- 27.85457 = 4*5*sqrt(1+(2*sin((pi/2)-0.959931088596701)*cos((pi/2)-0.959931088596701))).

How to calculate Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth?

With Circumradius of Rectangle (r_c) & Angle between Diagonal and Breadth of Rectangle (∠_db) we can find Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth using the formula - Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin((pi/2)-Angle between Diagonal and Breadth of Rectangle)*cos((pi/2)-Angle between Diagonal and Breadth of Rectangle))). 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 Circumradius and Angle between Diagonal and Breadth be negative?

No, the Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth, measured in Length cannot be negative.

Which unit is used to measure Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth?

Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth 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 Circumradius and Angle between Diagonal and Breadth can be measured.

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