Perimeter of Rhombus given Inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus)
P = (8*ri)/sin(Acute)
This formula uses 1 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)
Variables Used
Perimeter of Rhombus - (Measured in Meter) - The Perimeter of Rhombus is the total distance around the edge of the Rhombus.
Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
Acute Angle of Rhombus - (Measured in Radian) - Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.
STEP 1: Convert Input(s) to Base Unit
Inradius of Rhombus: 3 Meter --> 3 Meter No Conversion Required
Acute Angle of Rhombus: 45 Degree --> 0.785398163397301 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (8*ri)/sin(∠Acute) --> (8*3)/sin(0.785398163397301)
Evaluating ... ...
P = 33.9411254969593
STEP 3: Convert Result to Output's Unit
33.9411254969593 Meter --> No Conversion Required
FINAL ANSWER
33.9411254969593 33.94113 Meter <-- Perimeter of Rhombus
(Calculation completed in 00.004 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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Mumbai University (DJSCE), Mumbai
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9 Perimeter of Rhombus Calculators

Perimeter of Rhombus given Area
​ Go Perimeter of Rhombus = 4*sqrt(Area of Rhombus/sin(Acute Angle of Rhombus))
Perimeter of Rhombus given Short Diagonal and Long Diagonal
​ Go Perimeter of Rhombus = 2*sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2)
Perimeter of Rhombus given Short Diagonal and Obtuse Angle
​ Go Perimeter of Rhombus = (2*Short Diagonal of Rhombus)/cos(Obtuse Angle of Rhombus/2)
Perimeter of Rhombus given Long Diagonal and Obtuse Angle
​ Go Perimeter of Rhombus = (2*Long Diagonal of Rhombus)/sin(Obtuse Angle of Rhombus/2)
Perimeter of Rhombus given Short Diagonal
​ Go Perimeter of Rhombus = (2*Short Diagonal of Rhombus)/sin(Acute Angle of Rhombus/2)
Perimeter of Rhombus given Long Diagonal
​ Go Perimeter of Rhombus = (2*Long Diagonal of Rhombus)/cos(Acute Angle of Rhombus/2)
Perimeter of Rhombus given Inradius
​ Go Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus)
Perimeter of Rhombus given Height
​ Go Perimeter of Rhombus = (4*Height of Rhombus)/sin(Acute Angle of Rhombus)
Perimeter of Rhombus
​ Go Perimeter of Rhombus = 4*Side of Rhombus

Perimeter of Rhombus given Inradius Formula

Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus)
P = (8*ri)/sin(Acute)

What is a Rhombus?

A Rhombus is a special case of a parallelogram. In a Rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a Rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or Rhombus diamond. The plural form of a Rhombus is Rhombi or Rhombuses.

What is Perimeter of a Rhombus?

A rhombus is a quadrilateral whose four sides all have the same length. Another name of it is equilateral quadrilateral and is often called as a diamond or diamond-shaped object. The perimeter of a rhombus is the total distance travelled along the border of a rhombus.

How to Calculate Perimeter of Rhombus given Inradius?

Perimeter of Rhombus given Inradius calculator uses Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus) to calculate the Perimeter of Rhombus, The Perimeter of Rhombus given Inradius formula is defined as the total distance around the edge of the Rhombus, calculated using the inradius of the Rhombus. Perimeter of Rhombus is denoted by P symbol.

How to calculate Perimeter of Rhombus given Inradius using this online calculator? To use this online calculator for Perimeter of Rhombus given Inradius, enter Inradius of Rhombus (ri) & Acute Angle of Rhombus (∠Acute) and hit the calculate button. Here is how the Perimeter of Rhombus given Inradius calculation can be explained with given input values -> 33.94113 = (8*3)/sin(0.785398163397301).

FAQ

What is Perimeter of Rhombus given Inradius?
The Perimeter of Rhombus given Inradius formula is defined as the total distance around the edge of the Rhombus, calculated using the inradius of the Rhombus and is represented as P = (8*ri)/sin(∠Acute) or Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus). The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus & Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.
How to calculate Perimeter of Rhombus given Inradius?
The Perimeter of Rhombus given Inradius formula is defined as the total distance around the edge of the Rhombus, calculated using the inradius of the Rhombus is calculated using Perimeter of Rhombus = (8*Inradius of Rhombus)/sin(Acute Angle of Rhombus). To calculate Perimeter of Rhombus given Inradius, you need Inradius of Rhombus (ri) & Acute Angle of Rhombus (∠Acute). With our tool, you need to enter the respective value for Inradius of Rhombus & Acute Angle of Rhombus 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 Rhombus?
In this formula, Perimeter of Rhombus uses Inradius of Rhombus & Acute Angle of Rhombus. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Perimeter of Rhombus = 4*Side of Rhombus
  • Perimeter of Rhombus = 4*sqrt(Area of Rhombus/sin(Acute Angle of Rhombus))
  • Perimeter of Rhombus = (2*Long Diagonal of Rhombus)/cos(Acute Angle of Rhombus/2)
  • Perimeter of Rhombus = (2*Short Diagonal of Rhombus)/sin(Acute Angle of Rhombus/2)
  • Perimeter of Rhombus = (2*Long Diagonal of Rhombus)/sin(Obtuse Angle of Rhombus/2)
  • Perimeter of Rhombus = (2*Short Diagonal of Rhombus)/cos(Obtuse Angle of Rhombus/2)
  • Perimeter of Rhombus = 2*sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2)
  • Perimeter of Rhombus = (4*Height of Rhombus)/sin(Acute Angle of Rhombus)
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