Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length Calculator

✖Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.ⓘ Perimeter of Rectangle [P]			+10% -10%
✖Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.ⓘ Angle between Diagonal and Length of Rectangle [∠_dl]			+10% -10%

✖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 given Perimeter and Angle between Diagonal and Length [r_c]

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

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle))))
r_c = 1/2*(P/2*1/(sqrt(1+sin(2*∠_dl))))
This formula uses 2 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)
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

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.
Perimeter of Rectangle - (Measured in Meter) - Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Angle between Diagonal and Length of Rectangle - (Measured in Radian) - Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Rectangle: 28 Meter --> 28 Meter No Conversion Required
Angle between Diagonal and Length of Rectangle: 35 Degree --> 0.610865238197901 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = 1/2*(P/2*1/(sqrt(1+sin(2*∠_dl)))) --> 1/2*(28/2*1/(sqrt(1+sin(2*0.610865238197901))))

Evaluating ... ...

r_c = 5.02610530143194

STEP 3: Convert Result to Output's Unit

5.02610530143194 Meter --> No Conversion Required

FINAL ANSWER

5.02610530143194 ≈ 5.026105 Meter <-- Circumradius of Rectangle

(Calculation completed in 00.008 seconds)

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< Circumradius of Rectangle Calculators

Circumradius of Rectangle given Perimeter and Breadth

LaTeX Go Circumradius of Rectangle = sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Breadth of Rectangle)+(8*Breadth of Rectangle^2))/4

Circumradius of Rectangle given Perimeter and Length

LaTeX Go Circumradius of Rectangle = sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Length of Rectangle)+(8*Length of Rectangle^2))/4

Circumradius of Rectangle

LaTeX Go Circumradius of Rectangle = sqrt(Length of Rectangle^2+Breadth of Rectangle^2)/2

Circumradius of Rectangle given Diagonal

LaTeX Go Circumradius of Rectangle = Diagonal of Rectangle/2

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

LaTeX Go

Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle))))
r_c = 1/2*(P/2*1/(sqrt(1+sin(2*∠_dl))))

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 Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length?

Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length calculator uses Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle)))) to calculate the Circumradius of Rectangle, The Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length formula is defined as the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and angle between diagonal and length of the Rectangle. Circumradius of Rectangle is denoted by r_c symbol.

How to calculate Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length using this online calculator? To use this online calculator for Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length, enter Perimeter of Rectangle (P) & Angle between Diagonal and Length of Rectangle (∠_dl) and hit the calculate button. Here is how the Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length calculation can be explained with given input values -> 5.026105 = 1/2*(28/2*1/(sqrt(1+sin(2*0.610865238197901)))).

FAQ

What is Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length?

The Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length formula is defined as the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and angle between diagonal and length of the Rectangle and is represented as r_c = 1/2*(P/2*1/(sqrt(1+sin(2*∠_dl)))) or Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle)))). Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle & Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.

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

The Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length formula is defined as the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and angle between diagonal and length of the Rectangle is calculated using Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle)))). To calculate Circumradius of Rectangle given Perimeter and Angle between Diagonal and Length, you need Perimeter of Rectangle (P) & Angle between Diagonal and Length of Rectangle (∠_dl). With our tool, you need to enter the respective value for Perimeter of Rectangle & Angle between Diagonal and Length 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 Circumradius of Rectangle?

In this formula, Circumradius of Rectangle uses Perimeter of Rectangle & Angle between Diagonal and Length of Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Circumradius of Rectangle = sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Length of Rectangle)+(8*Length of Rectangle^2))/4
Circumradius of Rectangle = sqrt(Length of Rectangle^2+Breadth of Rectangle^2)/2
Circumradius of Rectangle = sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Breadth of Rectangle)+(8*Breadth of Rectangle^2))/4

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