Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
P = 4*rc*sqrt(1+(2*sin(d(Acute)/2)*cos(d(Acute)/2)))
This formula uses 3 Functions, 3 Variables
Functions Used
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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)
Variables Used
Perimeter of Rectangle - (Measured in Meter) - Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Circumradius of Rectangle - (Measured in Meter) - Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.
Acute Angle between Diagonals of Rectangle - (Measured in Radian) - Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Rectangle: 5 Meter --> 5 Meter No Conversion Required
Acute Angle between Diagonals of Rectangle: 70 Degree --> 1.2217304763958 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = 4*rc*sqrt(1+(2*sin(∠d(Acute)/2)*cos(∠d(Acute)/2))) --> 4*5*sqrt(1+(2*sin(1.2217304763958/2)*cos(1.2217304763958/2)))
Evaluating ... ...
P = 27.8545696128002
STEP 3: Convert Result to Output's Unit
27.8545696128002 Meter --> No Conversion Required
FINAL ANSWER
27.8545696128002 27.85457 Meter <-- Perimeter of Rectangle
(Calculation completed in 00.004 seconds)

Credits

Created by Bhavya Mutyala
Osmania University (OU), Hyderabad
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The National Institute of Engineering (NIE), Mysuru
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25 Perimeter of Rectangle Calculators

Perimeter of Rectangle given Area and Obtuse Angle between Diagonals
Go Perimeter of Rectangle = 2*sqrt(Area of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2)*sec((pi-Obtuse Angle between Diagonals of Rectangle)/2)+(2*Area of Rectangle))
Perimeter of Rectangle given Circumradius and Angle between Diagonal and Breadth
Go 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)))
Perimeter of Rectangle given Diagonal and Angle between Diagonal and Breadth
Go Perimeter of Rectangle = 2*Diagonal 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)))
Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals
Go Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2)))
Perimeter of Rectangle given Diagonal and Obtuse Angle between Diagonals
Go Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2)))
Perimeter of Rectangle given Area and Angle between Diagonal and Breadth
Go Perimeter of Rectangle = 2*sqrt((Area of Rectangle*sec(Angle between Diagonal and Breadth of Rectangle)*cosec(Angle between Diagonal and Breadth of Rectangle))+(2*Area of Rectangle))
Perimeter of Rectangle given Area and Angle between Diagonal and Length
Go Perimeter of Rectangle = 2*sqrt((Area of Rectangle*sec(Angle between Diagonal and Length of Rectangle)*cosec(Angle between Diagonal and Length of Rectangle))+(2*Area of Rectangle))
Perimeter of Rectangle given Area and Acute Angle between Diagonals
Go Perimeter of Rectangle = 2*sqrt(Area of Rectangle*cosec(Acute Angle between Diagonals of Rectangle/2)*sec(Acute Angle between Diagonals of Rectangle/2)+(2*Area of Rectangle))
Perimeter of Rectangle given Diameter of Circumcircle and Angle between Diagonal and Length
Go Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
Perimeter of Rectangle given Circumradius and Angle between Diagonal and Length
Go Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
Perimeter of Rectangle given Diagonal and Angle between Diagonal and Length
Go Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals
Go Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
Perimeter of Rectangle given Diagonal and Acute Angle between Diagonals
Go Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
Perimeter of Rectangle given Breadth and Diameter of Circumcircle
Go Perimeter of Rectangle = 2*(Breadth of Rectangle+sqrt(Diameter of Circumcircle of Rectangle^2-Breadth of Rectangle^2))
Perimeter of Rectangle given Length and Diameter of Circumcircle
Go Perimeter of Rectangle = 2*(Length of Rectangle+sqrt(Diameter of Circumcircle of Rectangle^2-Length of Rectangle^2))
Perimeter of Rectangle given Breadth and Circumradius
Go Perimeter of Rectangle = 2*(Breadth of Rectangle+sqrt((4*Circumradius of Rectangle^2)-Breadth of Rectangle^2))
Perimeter of Rectangle given Length and Circumradius
Go Perimeter of Rectangle = 2*(Length of Rectangle+sqrt((4*Circumradius of Rectangle^2)-Length of Rectangle^2))
Perimeter of Rectangle given Diagonal and Breadth
Go Perimeter of Rectangle = 2*(sqrt(Diagonal of Rectangle^2-Breadth of Rectangle^2)+Breadth of Rectangle)
Perimeter of Rectangle given Diagonal and Length
Go Perimeter of Rectangle = 2*(Length of Rectangle+sqrt(Diagonal of Rectangle^2-Length of Rectangle^2))
Perimeter of Rectangle given Area and Diameter of Circumcircle
Go Perimeter of Rectangle = 2*sqrt(Diameter of Circumcircle of Rectangle^2+(2*Area of Rectangle))
Perimeter of Rectangle given Area and Breadth
Go Perimeter of Rectangle = 2*((Area of Rectangle/Breadth of Rectangle)+Breadth of Rectangle)
Perimeter of Rectangle given Area and Length
Go Perimeter of Rectangle = (2*(Area of Rectangle+Length of Rectangle^2))/Length of Rectangle
Perimeter of Rectangle given Area and Circumradius
Go Perimeter of Rectangle = 2*sqrt((2*Area of Rectangle)+(4*Circumradius of Rectangle^2))
Perimeter of Rectangle given Area and Diagonal
Go Perimeter of Rectangle = 2*sqrt(Diagonal of Rectangle^2+(2*Area of Rectangle))
Perimeter of Rectangle
Go Perimeter of Rectangle = 2*(Length of Rectangle+Breadth of Rectangle)

Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Formula

Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
P = 4*rc*sqrt(1+(2*sin(d(Acute)/2)*cos(d(Acute)/2)))

What is a Rectangle?

A Rectangle is a two dimensional geometric shape having four sides and four corners. The four sides are in two pairs, in which each pair of lines are equal in length and parallel to each other. And adjacent sides are perpendicular to each other. In general a 2D shape with four boundary edges are called quadrilaterals. So a rectangle is a quadrilateral in which each corner is right angle.

How to Calculate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?

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

How to calculate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals using this online calculator? To use this online calculator for Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals, enter Circumradius of Rectangle (rc) & Acute Angle between Diagonals of Rectangle (∠d(Acute)) and hit the calculate button. Here is how the Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals calculation can be explained with given input values -> 27.85457 = 4*5*sqrt(1+(2*sin(1.2217304763958/2)*cos(1.2217304763958/2))).

FAQ

What is Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?
The Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Acute Angle between Diagonals of the Rectangle and is represented as P = 4*rc*sqrt(1+(2*sin(∠d(Acute)/2)*cos(∠d(Acute)/2))) or Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2))). Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle & Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.
How to calculate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?
The Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Acute Angle between Diagonals of the Rectangle is calculated using Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2))). To calculate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals, you need Circumradius of Rectangle (rc) & Acute Angle between Diagonals of Rectangle (∠d(Acute)). With our tool, you need to enter the respective value for Circumradius of Rectangle & Acute Angle between Diagonals of Rectangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Perimeter of Rectangle?
In this formula, Perimeter of Rectangle uses Circumradius of Rectangle & Acute Angle between Diagonals of Rectangle. We can use 35 other way(s) to calculate the same, which is/are as follows -
  • 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
  • Perimeter of Rectangle = 2*(Breadth of Rectangle+sqrt((4*Circumradius of Rectangle^2)-Breadth of Rectangle^2))
  • Perimeter of Rectangle = 2*(Breadth of Rectangle+sqrt(Diameter of Circumcircle of Rectangle^2-Breadth of Rectangle^2))
  • Perimeter of Rectangle = 2*(sqrt(Diagonal of Rectangle^2-Breadth of Rectangle^2)+Breadth of Rectangle)
  • Perimeter of Rectangle = 2*(Length of Rectangle+sqrt((4*Circumradius of Rectangle^2)-Length of Rectangle^2))
  • Perimeter of Rectangle = 2*(Length of Rectangle+sqrt(Diameter of Circumcircle of Rectangle^2-Length of Rectangle^2))
  • Perimeter of Rectangle = 2*((Area of Rectangle/Breadth of Rectangle)+Breadth of Rectangle)
  • Perimeter of Rectangle = 2*sqrt(Diagonal of Rectangle^2+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*sqrt((2*Area of Rectangle)+(4*Circumradius of Rectangle^2))
  • Perimeter of Rectangle = 2*sqrt(Diameter of Circumcircle of Rectangle^2+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*sqrt((Area of Rectangle*sec(Angle between Diagonal and Length of Rectangle)*cosec(Angle between Diagonal and Length of Rectangle))+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*sqrt((Area of Rectangle*sec(Angle between Diagonal and Breadth of Rectangle)*cosec(Angle between Diagonal and Breadth of Rectangle))+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*sqrt(Area of Rectangle*cosec(Acute Angle between Diagonals of Rectangle/2)*sec(Acute Angle between Diagonals of Rectangle/2)+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*sqrt(Area of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2)*sec((pi-Obtuse Angle between Diagonals of Rectangle)/2)+(2*Area of Rectangle))
  • Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
  • Perimeter of Rectangle = 2*Diagonal 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)))
  • Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
  • Perimeter of Rectangle = 2*Diagonal of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2)))
  • 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)))
  • Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
  • Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin((pi-Obtuse Angle between Diagonals of Rectangle)/2)*cos((pi-Obtuse Angle between Diagonals of Rectangle)/2)))
  • Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin(Angle between Diagonal and Length of Rectangle)*cos(Angle between Diagonal and Length of Rectangle)))
  • Perimeter of Rectangle = 2*Diameter of Circumcircle 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)))
  • Perimeter of Rectangle = 2*Diameter of Circumcircle of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2)))
  • 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)))
  • Perimeter of Rectangle = 2*Length of Rectangle*(1+tan(Angle between Diagonal and Length of Rectangle))
  • Perimeter of Rectangle = 2*Length of Rectangle*(1+tan((pi/2)-Angle between Diagonal and Breadth of Rectangle))
  • Perimeter of Rectangle = 2*Length of Rectangle*(1+tan((pi-Obtuse Angle between Diagonals of Rectangle)/2))
  • Perimeter of Rectangle = 2*Length of Rectangle*(1+tan(Acute Angle between Diagonals of Rectangle/2))
  • Perimeter of Rectangle = 2*Breadth of Rectangle*(1+cot(Angle between Diagonal and Length of Rectangle))
  • Perimeter of Rectangle = 2*Breadth of Rectangle*(1+cot((pi/2)-Angle between Diagonal and Breadth of Rectangle))
  • Perimeter of Rectangle = 2*Breadth of Rectangle*(1+cot((pi-Obtuse Angle between Diagonals of Rectangle)/2))
  • Perimeter of Rectangle = 2*Breadth of Rectangle*(1+cot(Acute Angle between Diagonals of Rectangle/2))
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