Long Diagonal of Rhombus given Perimeter Calculator

✖The Perimeter of Rhombus is the total distance around the edge of the Rhombus.ⓘ Perimeter of Rhombus [P]			+10% -10%
✖Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.ⓘ Acute Angle of Rhombus [∠_Acute]			+10% -10%

✖The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.ⓘ Long Diagonal of Rhombus given Perimeter [d_Long]

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Formula

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Long Diagonal of Rhombus given Perimeter

Formula

`"d"_{"Long"} = "P"/2*cos("∠"_{"Acute"}/2)`

Example

`"18.47759m"="40m"/2*cos("45°"/2)`

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Long Diagonal of Rhombus given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2)
d_Long = P/2*cos(∠_Acute/2)
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

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.
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

d_Long = P/2*cos(∠_Acute/2) --> 40/2*cos(0.785398163397301/2)

Evaluating ... ...

d_Long = 18.4775906502263

STEP 3: Convert Result to Output's Unit

18.4775906502263 Meter --> No Conversion Required

FINAL ANSWER

18.4775906502263 ≈ 18.47759 Meter <-- Long Diagonal of Rhombus

(Calculation completed in 00.020 seconds)

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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 Long Diagonal of Rhombus Calculators

Long Diagonal of Rhombus given Area

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

Long Diagonal of Rhombus given Short Diagonal and Acute Angle

Go Long Diagonal of Rhombus = Short Diagonal of Rhombus/tan(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Short Diagonal and Side

Go Long Diagonal of Rhombus = sqrt(4*Side of Rhombus^2-Short Diagonal of Rhombus^2)

Long Diagonal of Rhombus given Inradius

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

Long Diagonal of Rhombus given Perimeter

Go Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Obtuse angle

Go Long Diagonal of Rhombus = 2*Side of Rhombus*sin(Obtuse Angle of Rhombus/2)

Long Diagonal of Rhombus given Height

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

Long Diagonal of Rhombus

Go Long Diagonal of Rhombus = 2*Side of Rhombus*cos(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Area and Short Diagonal

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

Long Diagonal of Rhombus given Perimeter Formula

Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2)
d_Long = P/2*cos(∠_Acute/2)

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 Long Diagonal of Rhombus given Perimeter?

Long Diagonal of Rhombus given Perimeter calculator uses Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2) to calculate the Long Diagonal of Rhombus, The Long Diagonal of Rhombus given Perimeter formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the perimeter of the Rhombus. Long Diagonal of Rhombus is denoted by d_Long symbol.

How to calculate Long Diagonal of Rhombus given Perimeter using this online calculator? To use this online calculator for Long Diagonal of Rhombus given Perimeter, enter Perimeter of Rhombus (P) & Acute Angle of Rhombus (∠_Acute) and hit the calculate button. Here is how the Long Diagonal of Rhombus given Perimeter calculation can be explained with given input values -> 18.47759 = 40/2*cos(0.785398163397301/2).

FAQ

What is Long Diagonal of Rhombus given Perimeter?

The Long Diagonal of Rhombus given Perimeter formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the perimeter of the Rhombus and is represented as d_Long = P/2*cos(∠_Acute/2) or Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2). 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 Long Diagonal of Rhombus given Perimeter?

The Long Diagonal of Rhombus given Perimeter formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the perimeter of the Rhombus is calculated using Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2). To calculate Long Diagonal 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 Long Diagonal of Rhombus?

In this formula, Long Diagonal of Rhombus uses Perimeter of Rhombus & Acute Angle of Rhombus. We can use 8 other way(s) to calculate the same, which is/are as follows -

Long Diagonal of Rhombus = 2*Side of Rhombus*sin(Obtuse Angle of Rhombus/2)
Long Diagonal of Rhombus = 2*Side of Rhombus*cos(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = Short Diagonal of Rhombus/tan(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = sqrt(4*Side of Rhombus^2-Short Diagonal of Rhombus^2)
Long Diagonal of Rhombus = (2*Area of Rhombus)/(Short Diagonal of Rhombus)
Long Diagonal of Rhombus = Area of Rhombus/(Side of Rhombus*sin(Acute Angle of Rhombus/2))
Long Diagonal of Rhombus = Height of Rhombus/sin(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2)

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