Inradius of Rhombus given Short Diagonal and Side Calculator

✖A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.ⓘ Short Diagonal of Rhombus [d_Short]			+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 Short Diagonal and Side [r_i]

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Formula

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Inradius of Rhombus given Short Diagonal and Side

Formula

`"r"_{"i"} = ("d"_{"Short"}*sqrt("S"^2-"d"_{"Short"}^2/4))/(2*"S")`

Example

`"3.666061m"=("8m"*sqrt(("10m")^2-("8m")^2/4))/(2*"10m")`

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Inradius of Rhombus given Short Diagonal and Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Rhombus = (Short Diagonal of Rhombus*sqrt(Side of Rhombus^2-Short Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
r_i = (d_Short*sqrt(S^2-d_Short^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.
Short Diagonal of Rhombus - (Measured in Meter) - A Short Diagonal of Rhombus is a length of the line joining the obtuse 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

Short Diagonal of Rhombus: 8 Meter --> 8 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_Short*sqrt(S^2-d_Short^2/4))/(2*S) --> (8*sqrt(10^2-8^2/4))/(2*10)

Evaluating ... ...

r_i = 3.66606055596467

STEP 3: Convert Result to Output's Unit

3.66606055596467 Meter --> No Conversion Required

FINAL ANSWER

3.66606055596467 ≈ 3.666061 Meter <-- Inradius of Rhombus

(Calculation completed in 00.004 seconds)

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< 10+ Inradius of Rhombus Calculators

Inradius of Rhombus given both Diagonals

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 Short Diagonal and Side

Go 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

Go 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

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

Inradius of Rhombus given Short Diagonal and Acute Angle

Go Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2)

Inradius of Rhombus given Long Diagonal and Acute Angle

Go Inradius of Rhombus = Long Diagonal of Rhombus/2*sin(Acute Angle of Rhombus/2)

Inradius of Rhombus given Perimeter

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

Inradius of Rhombus

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

Inradius of Rhombus given Area and Side

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

Inradius of Rhombus given Height

Go Inradius of Rhombus = Height of Rhombus/2

< 6 Inradius of Rhombus Calculators

Inradius of Rhombus given both Diagonals

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 Short Diagonal and Side

Go 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

Go 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

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

Inradius of Rhombus given Area and Side

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

Inradius of Rhombus given Height

Go Inradius of Rhombus = Height of Rhombus/2

Inradius of Rhombus given Short Diagonal and Side Formula

Inradius of Rhombus = (Short Diagonal of Rhombus*sqrt(Side of Rhombus^2-Short Diagonal of Rhombus^2/4))/(2*Side of Rhombus)
r_i = (d_Short*sqrt(S^2-d_Short^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. From this, it follows that the center of the incircle together with the many excircle centers form an orthocentric system.

How to Calculate Inradius of Rhombus given Short Diagonal and Side?

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

How to calculate Inradius of Rhombus given Short Diagonal and Side using this online calculator? To use this online calculator for Inradius of Rhombus given Short Diagonal and Side, enter Short Diagonal of Rhombus (d_Short) & Side of Rhombus (S) and hit the calculate button. Here is how the Inradius of Rhombus given Short Diagonal and Side calculation can be explained with given input values -> 3.666061 = (8*sqrt(10^2-8^2/4))/(2*10).

FAQ

What is Inradius of Rhombus given Short Diagonal and Side?

Inradius of Rhombus given Short Diagonal and Side is defined as the radius of the inscribed circle of the Rhombus, calculated using a short diagonal and side of the Rhombus and is represented as r_i = (d_Short*sqrt(S^2-d_Short^2/4))/(2*S) or Inradius of Rhombus = (Short Diagonal of Rhombus*sqrt(Side of Rhombus^2-Short Diagonal of Rhombus^2/4))/(2*Side of Rhombus). A Short Diagonal of Rhombus is a length of the line joining the obtuse 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 Short Diagonal and Side?

Inradius of Rhombus given Short Diagonal and Side is defined as the radius of the inscribed circle of the Rhombus, calculated using a short diagonal and side of the Rhombus is calculated using Inradius of Rhombus = (Short Diagonal of Rhombus*sqrt(Side of Rhombus^2-Short Diagonal of Rhombus^2/4))/(2*Side of Rhombus). To calculate Inradius of Rhombus given Short Diagonal and Side, you need Short Diagonal of Rhombus (d_Short) & Side of Rhombus (S). With our tool, you need to enter the respective value for Short 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 Short Diagonal of Rhombus & Side of Rhombus. We can use 14 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 = Height 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 = Area of Rhombus/(2*Side of Rhombus)
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 = Height 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)

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