Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals Calculator

✖Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.ⓘ Circumradius of Rectangle [r_c]			+10% -10%
✖Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.ⓘ Obtuse Angle between Diagonals of Rectangle [∠_d(Obtuse)]			+10% -10%

✖Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.ⓘ Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals [P]

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Formula

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Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals

Formula

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

Example

27.85457 m = 4 \cdot 5 m \cdot \sqrt{1 + (2 \cdot \sin (\frac{π - 110 °}{2}) \cdot \cos (\frac{π - 110 °}{2}))}

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Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
P = 4*r_c*sqrt(1+(2*sin((pi-∠_d(Obtuse))/2)*cos((pi-∠_d(Obtuse))/2)))
This formula uses 1 Constants, 3 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Obtuse Angle between Diagonals of Rectangle - (Measured in Radian) - Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Rectangle: 5 Meter --> 5 Meter No Conversion Required
Obtuse Angle between Diagonals of Rectangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = 4*r_c*sqrt(1+(2*sin((pi-∠_d(Obtuse))/2)*cos((pi-∠_d(Obtuse))/2))) --> 4*5*sqrt(1+(2*sin((pi-1.9198621771934)/2)*cos((pi-1.9198621771934)/2)))

Evaluating ... ...

P = 27.8545696128016

STEP 3: Convert Result to Output's Unit

27.8545696128016 Meter --> No Conversion Required

FINAL ANSWER

27.8545696128016 ≈ 27.85457 Meter <-- Perimeter of Rectangle

(Calculation completed in 00.004 seconds)

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Created by Bhavya Mutyala

Osmania University (OU), Hyderabad

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< Perimeter of Rectangle Calculators

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 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 Length

Go Perimeter of Rectangle = (2*(Area of Rectangle+Length of Rectangle^2))/Length of Rectangle

Perimeter of Rectangle

Go Perimeter of Rectangle = 2*(Length of Rectangle+Breadth of Rectangle)

Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals Formula

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 Obtuse Angle between Diagonals?

Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals calculator uses 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))) to calculate the Perimeter of Rectangle, The Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Obtuse Angle between Diagonals of the Rectangle. Perimeter of Rectangle is denoted by P symbol.

How to calculate Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals using this online calculator? To use this online calculator for Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals, enter Circumradius of Rectangle (r_c) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) and hit the calculate button. Here is how the Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals calculation can be explained with given input values -> 27.85457 = 4*5*sqrt(1+(2*sin((pi-1.9198621771934)/2)*cos((pi-1.9198621771934)/2))).

FAQ

What is Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals?

The Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Obtuse Angle between Diagonals of the Rectangle and is represented as P = 4*r_c*sqrt(1+(2*sin((pi-∠_d(Obtuse))/2)*cos((pi-∠_d(Obtuse))/2))) or 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))). Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle & Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

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

The Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Obtuse Angle between Diagonals of the Rectangle is calculated using 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))). To calculate Perimeter of Rectangle given Circumradius and Obtuse Angle between Diagonals, you need Circumradius of Rectangle (r_c) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)). With our tool, you need to enter the respective value for Circumradius of Rectangle & Obtuse 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 & Obtuse Angle between Diagonals of Rectangle. We can use 3 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

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