Area 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%

✖Area of Rhombus is the amount of two-dimensional space occupied by the Rhombus.ⓘ Area of Rhombus given Perimeter [A]

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Formula

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Area of Rhombus given Perimeter

Formula

`"A" = ("P"/4)^2*sin("∠"_{"Acute"})`

Example

`"70.71068m²"=("40m"/4)^2*sin("45°")`

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Area of Rhombus given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Area of Rhombus - (Measured in Square Meter) - Area of Rhombus is the amount of two-dimensional space occupied by 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

A = (P/4)^2*sin(∠_Acute) --> (40/4)^2*sin(0.785398163397301)

Evaluating ... ...

A = 70.7106781186443

STEP 3: Convert Result to Output's Unit

70.7106781186443 Square Meter --> No Conversion Required

FINAL ANSWER

70.7106781186443 ≈ 70.71068 Square Meter <-- Area 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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< 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 Perimeter Formula

Area of Rhombus = (Perimeter of Rhombus/4)^2*sin(Acute Angle of Rhombus)
A = (P/4)^2*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.

How to Calculate Area of Rhombus given Perimeter?

Area of Rhombus given Perimeter calculator uses Area of Rhombus = (Perimeter of Rhombus/4)^2*sin(Acute Angle of Rhombus) to calculate the Area of Rhombus, The Area of Rhombus given Perimeter formula is defined as the amount of 2-dimensional space included within the boundary of the Rhombus, calculated using the perimeter of the Rhombus. Area of Rhombus is denoted by A symbol.

How to calculate Area of Rhombus given Perimeter using this online calculator? To use this online calculator for Area of Rhombus given Perimeter, enter Perimeter of Rhombus (P) & Acute Angle of Rhombus (∠_Acute) and hit the calculate button. Here is how the Area of Rhombus given Perimeter calculation can be explained with given input values -> 70.71068 = (40/4)^2*sin(0.785398163397301).

FAQ

What is Area of Rhombus given Perimeter?

The Area of Rhombus given Perimeter formula is defined as the amount of 2-dimensional space included within the boundary of the Rhombus, calculated using the perimeter of the Rhombus and is represented as A = (P/4)^2*sin(∠_Acute) or Area of Rhombus = (Perimeter of Rhombus/4)^2*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 Area of Rhombus given Perimeter?

The Area of Rhombus given Perimeter formula is defined as the amount of 2-dimensional space included within the boundary of the Rhombus, calculated using the perimeter of the Rhombus is calculated using Area of Rhombus = (Perimeter of Rhombus/4)^2*sin(Acute Angle of Rhombus). To calculate Area 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 Area of Rhombus?

In this formula, Area of Rhombus uses Perimeter of Rhombus & Acute 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 = (4*Inradius of Rhombus^2)/sin(Obtuse Angle of Rhombus)
Area of Rhombus = Side of Rhombus*Height of Rhombus
Area of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/2

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