Area of Rhombus given Inradius and Obtuse Angle Calculator

✖The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.ⓘ Inradius of Rhombus [r_i]			+10% -10%
✖Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree.ⓘ Obtuse Angle of Rhombus [∠_Obtuse]			+10% -10%

✖Area of Rhombus is the amount of two-dimensional space occupied by the Rhombus.ⓘ Area of Rhombus given Inradius and Obtuse Angle [A]

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Formula

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Area of Rhombus given Inradius and Obtuse Angle

Formula

`"A" = (4*"r"_{"i"}^2)/sin("∠"_{"Obtuse"})`

Example

`"50.91169m²"=(4*("3m")^2)/sin("135°")`

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Area of Rhombus given Inradius and Obtuse Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus)
A = (4*r_i^2)/sin(∠_Obtuse)
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

Area of Rhombus - (Measured in Square Meter) - Area of Rhombus is the amount of two-dimensional space occupied by 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.
Obtuse Angle of Rhombus - (Measured in Radian) - Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree.

STEP 1: Convert Input(s) to Base Unit

Inradius of Rhombus: 3 Meter --> 3 Meter No Conversion Required
Obtuse Angle of Rhombus: 135 Degree --> 2.3561944901919 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (4*r_i^2)/sin(∠_Obtuse) --> (4*3^2)/sin(2.3561944901919)

Evaluating ... ...

A = 50.9116882454088

STEP 3: Convert Result to Output's Unit

50.9116882454088 Square Meter --> No Conversion Required

FINAL ANSWER

50.9116882454088 ≈ 50.91169 Square Meter <-- Area of Rhombus

(Calculation completed in 00.007 seconds)

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Indian Institute of Technology (IIT), Roorkee

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< 6 Area of Rhombus Calculators

Area of Rhombus given Inradius and Obtuse Angle

Go Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus)

Area of Rhombus given Perimeter

Go Area of Rhombus = (Perimeter of Rhombus/4)^2*sin(Acute Angle of Rhombus)

Area of Rhombus

Go Area of Rhombus = Side of Rhombus^2*sin(Acute Angle of Rhombus)

Area of Rhombus given Both Diagonals

Go Area of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/2

Area of Rhombus given Inradius

Go Area of Rhombus = 2*Side of Rhombus*Inradius of Rhombus

Area of Rhombus given Height

Go Area of Rhombus = Side of Rhombus*Height of Rhombus

Area of Rhombus given Inradius and Obtuse Angle Formula

Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus)
A = (4*r_i^2)/sin(∠_Obtuse)

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.

How to Calculate Area of Rhombus given Inradius and Obtuse Angle?

Area of Rhombus given Inradius and Obtuse Angle calculator uses Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus) to calculate the Area of Rhombus, Area of Rhombus given Inradius and Obtuse Angle can be defined as the amount of space included within the boundary of the Rhombus, calculated using the inradius and obtuse angle of the Rhombus. Area of Rhombus is denoted by A symbol.

How to calculate Area of Rhombus given Inradius and Obtuse Angle using this online calculator? To use this online calculator for Area of Rhombus given Inradius and Obtuse Angle, enter Inradius of Rhombus (r_i) & Obtuse Angle of Rhombus (∠_Obtuse) and hit the calculate button. Here is how the Area of Rhombus given Inradius and Obtuse Angle calculation can be explained with given input values -> 50.91169 = (4*3^2)/sin(2.3561944901919).

FAQ

What is Area of Rhombus given Inradius and Obtuse Angle?

Area of Rhombus given Inradius and Obtuse Angle can be defined as the amount of space included within the boundary of the Rhombus, calculated using the inradius and obtuse angle of the Rhombus and is represented as A = (4*r_i^2)/sin(∠_Obtuse) or Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus). The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus & Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree.

How to calculate Area of Rhombus given Inradius and Obtuse Angle?

Area of Rhombus given Inradius and Obtuse Angle can be defined as the amount of space included within the boundary of the Rhombus, calculated using the inradius and obtuse angle of the Rhombus is calculated using Area of Rhombus = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus). To calculate Area of Rhombus given Inradius and Obtuse Angle, you need Inradius of Rhombus (r_i) & Obtuse Angle of Rhombus (∠_Obtuse). With our tool, you need to enter the respective value for Inradius of Rhombus & Obtuse 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 Area of Rhombus?

In this formula, Area of Rhombus uses Inradius of Rhombus & Obtuse Angle of Rhombus. We can use 5 other way(s) to calculate the same, which is/are as follows -

Area of Rhombus = Side of Rhombus^2*sin(Acute Angle of Rhombus)
Area of Rhombus = 2*Side of Rhombus*Inradius of Rhombus
Area of Rhombus = Side of Rhombus*Height of Rhombus
Area of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/2
Area of Rhombus = (Perimeter of Rhombus/4)^2*sin(Acute Angle of Rhombus)

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