## Inradius of Rhombus given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inradius of Rhombus = Perimeter of Rhombus/8*sin(Acute Angle of Rhombus)
ri = P/8*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
Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
Perimeter of Rhombus - (Measured in Meter) - The Perimeter of Rhombus is the total distance around the edge of 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
Perimeter of Rhombus: 40 Meter --> 40 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
ri = P/8*sin(∠Acute) --> 40/8*sin(0.785398163397301)
Evaluating ... ...
ri = 3.53553390593222
STEP 3: Convert Result to Output's Unit
3.53553390593222 Meter --> No Conversion Required
3.53553390593222 3.535534 Meter <-- Inradius of Rhombus
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 10+ Inradius of Rhombus Calculators

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

## Inradius of Rhombus given Perimeter Formula

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

## What is 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 an Inscribed Circle?

In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. The center of the incircle is called the polygon's incenter.The center of the incircle can be found as the intersection of the many internal angle bisectors.

## How to Calculate Inradius of Rhombus given Perimeter?

Inradius of Rhombus given Perimeter calculator uses Inradius of Rhombus = Perimeter of Rhombus/8*sin(Acute Angle of Rhombus) to calculate the Inradius of Rhombus, The Inradius of Rhombus given Perimeter formula is defined as the radius of the circle inscribed inside the Rhombus, calculated using the perimeter of the Rhombus. Inradius of Rhombus is denoted by ri symbol.

How to calculate Inradius of Rhombus given Perimeter using this online calculator? To use this online calculator for Inradius of Rhombus given Perimeter, enter Perimeter of Rhombus (P) & Acute Angle of Rhombus (∠Acute) and hit the calculate button. Here is how the Inradius of Rhombus given Perimeter calculation can be explained with given input values -> 3.535534 = 40/8*sin(0.785398163397301).

### FAQ

What is Inradius of Rhombus given Perimeter?
The Inradius of Rhombus given Perimeter formula is defined as the radius of the circle inscribed inside the Rhombus, calculated using the perimeter of the Rhombus and is represented as ri = P/8*sin(∠Acute) or Inradius of Rhombus = Perimeter of Rhombus/8*sin(Acute Angle of Rhombus). The Perimeter of Rhombus is the total distance around the edge of the Rhombus & Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.
How to calculate Inradius of Rhombus given Perimeter?
The Inradius of Rhombus given Perimeter formula is defined as the radius of the circle inscribed inside the Rhombus, calculated using the perimeter of the Rhombus is calculated using Inradius of Rhombus = Perimeter of Rhombus/8*sin(Acute Angle of Rhombus). To calculate Inradius of Rhombus given Perimeter, you need Perimeter of Rhombus (P) & Acute Angle of Rhombus (∠Acute). With our tool, you need to enter the respective value for Perimeter 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 Inradius of Rhombus?
In this formula, Inradius of Rhombus uses Perimeter of Rhombus & Acute Angle of Rhombus. We can use 9 other way(s) to calculate the same, which is/are as follows -
• Inradius of Rhombus = Area of Rhombus/(2*Side of Rhombus)
• Inradius of Rhombus = sqrt(Area of Rhombus*sin(Acute Angle of Rhombus))/2
• Inradius of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(2*sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))
• Inradius of Rhombus = (Side of Rhombus*sin(Acute Angle of Rhombus))/2
• Inradius of Rhombus = Long Diagonal of Rhombus/2*sin(Acute Angle of Rhombus/2)
• Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2)
• Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
• Inradius of Rhombus = (Short Diagonal of Rhombus*sqrt(Side of Rhombus^2-Short Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
• Inradius of Rhombus = Height of Rhombus/2
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