Inradius of Rhombus given Long Diagonal and Side Calculator

✖The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.ⓘ Long Diagonal of Rhombus [d_Long]			+10% -10%
✖The Side of Rhombus is the length of any of the four edges.ⓘ Side of Rhombus [S]			+10% -10%

✖The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.ⓘ Inradius of Rhombus given Long Diagonal and Side [r_i]

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Inradius of Rhombus given Long Diagonal and Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
r_i = (d_Long*sqrt(S^2-d_Long^2/4))/(2*S)
This formula uses 1 Functions, 3 Variables

Functions Used

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

Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
Long Diagonal of Rhombus - (Measured in Meter) - The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.
Side of Rhombus - (Measured in Meter) - The Side of Rhombus is the length of any of the four edges.

STEP 1: Convert Input(s) to Base Unit

Long Diagonal of Rhombus: 18 Meter --> 18 Meter No Conversion Required
Side of Rhombus: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (d_Long*sqrt(S^2-d_Long^2/4))/(2*S) --> (18*sqrt(10^2-18^2/4))/(2*10)

Evaluating ... ...

r_i = 3.92300904918661

STEP 3: Convert Result to Output's Unit

3.92300904918661 Meter --> No Conversion Required

FINAL ANSWER

3.92300904918661 ≈ 3.923009 Meter <-- Inradius of Rhombus

(Calculation completed in 00.007 seconds)

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< Inradius of Rhombus Calculators

Inradius of Rhombus given both Diagonals

LaTeX Go 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 Area and Acute Angle

LaTeX Go Inradius of Rhombus = sqrt(Area of Rhombus*sin(Acute Angle of Rhombus))/2

Inradius of Rhombus

LaTeX Go Inradius of Rhombus = (Side of Rhombus*sin(Acute Angle of Rhombus))/2

Inradius of Rhombus given Area and Side

LaTeX Go Inradius of Rhombus = Area of Rhombus/(2*Side of Rhombus)

< Inradius of Rhombus Calculators

Inradius of Rhombus given both Diagonals

LaTeX Go 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

LaTeX Go Inradius of Rhombus = (Side of Rhombus*sin(Acute Angle of Rhombus))/2

Inradius of Rhombus given Area and Side

LaTeX Go Inradius of Rhombus = Area of Rhombus/(2*Side of Rhombus)

Inradius of Rhombus given Height

LaTeX Go Inradius of Rhombus = Height of Rhombus/2

Inradius of Rhombus given Long Diagonal and Side Formula

LaTeX Go

Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
r_i = (d_Long*sqrt(S^2-d_Long^2/4))/(2*S)

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 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 Long Diagonal and Side?

Inradius of Rhombus given Long Diagonal and Side calculator uses Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus) to calculate the Inradius of Rhombus, Inradius of Rhombus given Long Diagonal and Side is defined as the radius of the inscribed circle of the Rhombus, calculated using the long diagonal and side of the Rhombus. Inradius of Rhombus is denoted by r_i symbol.

How to calculate Inradius of Rhombus given Long Diagonal and Side using this online calculator? To use this online calculator for Inradius of Rhombus given Long Diagonal and Side, enter Long Diagonal of Rhombus (d_Long) & Side of Rhombus (S) and hit the calculate button. Here is how the Inradius of Rhombus given Long Diagonal and Side calculation can be explained with given input values -> 3.923009 = (18*sqrt(10^2-18^2/4))/(2*10).

FAQ

What is Inradius of Rhombus given Long Diagonal and Side?

Inradius of Rhombus given Long Diagonal and Side is defined as the radius of the inscribed circle of the Rhombus, calculated using the long diagonal and side of the Rhombus and is represented as r_i = (d_Long*sqrt(S^2-d_Long^2/4))/(2*S) or Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus). The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus & The Side of Rhombus is the length of any of the four edges.

How to calculate Inradius of Rhombus given Long Diagonal and Side?

Inradius of Rhombus given Long Diagonal and Side is defined as the radius of the inscribed circle of the Rhombus, calculated using the long diagonal and side of the Rhombus is calculated using Inradius of Rhombus = (Long Diagonal of Rhombus*sqrt(Side of Rhombus^2-Long Diagonal of Rhombus^2/4))/(2*Side of Rhombus). To calculate Inradius of Rhombus given Long Diagonal and Side, you need Long Diagonal of Rhombus (d_Long) & Side of Rhombus (S). With our tool, you need to enter the respective value for Long Diagonal of Rhombus & Side 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 Long Diagonal of Rhombus & Side of Rhombus. We can use 3 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))

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