Area of Rectangle given Perimeter and Acute Angle between Diagonals Calculator

✖Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.ⓘ Perimeter of Rectangle [P]			+10% -10%
✖Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.ⓘ Acute Angle between Diagonals of Rectangle [∠_d(Acute)]			+10% -10%

✖Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.ⓘ Area of Rectangle given Perimeter and Acute Angle between Diagonals [A]

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Formula

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Area of Rectangle given Perimeter and Acute Angle between Diagonals

Formula

A = \frac{{(\frac{P}{2})}^{2}}{(\tan (\frac{∠ d(Acute)}{2}) + 1) \cdot (\cot (\frac{∠ d(Acute)}{2}) + 1)}

Example

47.47653 m² = \frac{{(\frac{28 m}{2})}^{2}}{(\tan (\frac{70 °}{2}) + 1) \cdot (\cot (\frac{70 °}{2}) + 1)}

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Area of Rectangle given Perimeter and Acute Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Rectangle = (Perimeter of Rectangle/2)^2/((tan(Acute Angle between Diagonals of Rectangle/2)+1)*(cot(Acute Angle between Diagonals of Rectangle/2)+1))
A = (P/2)^2/((tan(∠_d(Acute)/2)+1)*(cot(∠_d(Acute)/2)+1))
This formula uses 2 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)

Variables Used

Area of Rectangle - (Measured in Square Meter) - Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.
Perimeter of Rectangle - (Measured in Meter) - Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Acute Angle between Diagonals of Rectangle - (Measured in Radian) - Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Rectangle: 28 Meter --> 28 Meter No Conversion Required
Acute Angle between Diagonals of Rectangle: 70 Degree --> 1.2217304763958 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (P/2)^2/((tan(∠_d(Acute)/2)+1)*(cot(∠_d(Acute)/2)+1)) --> (28/2)^2/((tan(1.2217304763958/2)+1)*(cot(1.2217304763958/2)+1))

Evaluating ... ...

A = 47.4765309978355

STEP 3: Convert Result to Output's Unit

47.4765309978355 Square Meter --> No Conversion Required

FINAL ANSWER

47.4765309978355 ≈ 47.47653 Square Meter <-- Area of Rectangle

(Calculation completed in 00.004 seconds)

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< Area of Rectangle Calculators

Area of Rectangle given Breadth and Diagonal

Go Area of Rectangle = Breadth of Rectangle*sqrt(Diagonal of Rectangle^2-Breadth of Rectangle^2)

Area of Rectangle given Length and Diagonal

Go Area of Rectangle = Length of Rectangle*sqrt(Diagonal of Rectangle^2-Length of Rectangle^2)

Area of Rectangle given Perimeter and Length

Go Area of Rectangle = ((Perimeter of Rectangle*Length of Rectangle)-(2*Length of Rectangle^2))/2

Area of Rectangle

Go Area of Rectangle = Length of Rectangle*Breadth of Rectangle

Area of Rectangle given Perimeter and Acute Angle between Diagonals Formula

What is a Rectangle?

A Rectangle is a two dimensional geometric shape having four sides and four corners. The four sides are in two pairs, in which each pair of lines are equal in length and parallel to each other. And adjacent sides are perpendicular to each other. In general a 2D shape with four boundary edges are called quadrilaterals. So a rectangle is a quadrilateral in which each corner is right angle.

How to Calculate Area of Rectangle given Perimeter and Acute Angle between Diagonals?

Area of Rectangle given Perimeter and Acute Angle between Diagonals calculator uses Area of Rectangle = (Perimeter of Rectangle/2)^2/((tan(Acute Angle between Diagonals of Rectangle/2)+1)*(cot(Acute Angle between Diagonals of Rectangle/2)+1)) to calculate the Area of Rectangle, The Area of Rectangle given Perimeter and Acute Angle between Diagonals formula is defined as the total quantity of plane enclosed by the boundary of the Rectangle, and calculated using perimeter and acute angle between diagonals of Rectangle. Area of Rectangle is denoted by A symbol.

How to calculate Area of Rectangle given Perimeter and Acute Angle between Diagonals using this online calculator? To use this online calculator for Area of Rectangle given Perimeter and Acute Angle between Diagonals, enter Perimeter of Rectangle (P) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) and hit the calculate button. Here is how the Area of Rectangle given Perimeter and Acute Angle between Diagonals calculation can be explained with given input values -> 47.47653 = (28/2)^2/((tan(1.2217304763958/2)+1)*(cot(1.2217304763958/2)+1)).

FAQ

What is Area of Rectangle given Perimeter and Acute Angle between Diagonals?

The Area of Rectangle given Perimeter and Acute Angle between Diagonals formula is defined as the total quantity of plane enclosed by the boundary of the Rectangle, and calculated using perimeter and acute angle between diagonals of Rectangle and is represented as A = (P/2)^2/((tan(∠_d(Acute)/2)+1)*(cot(∠_d(Acute)/2)+1)) or Area of Rectangle = (Perimeter of Rectangle/2)^2/((tan(Acute Angle between Diagonals of Rectangle/2)+1)*(cot(Acute Angle between Diagonals of Rectangle/2)+1)). Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle & Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.

How to calculate Area of Rectangle given Perimeter and Acute Angle between Diagonals?

The Area of Rectangle given Perimeter and Acute Angle between Diagonals formula is defined as the total quantity of plane enclosed by the boundary of the Rectangle, and calculated using perimeter and acute angle between diagonals of Rectangle is calculated using Area of Rectangle = (Perimeter of Rectangle/2)^2/((tan(Acute Angle between Diagonals of Rectangle/2)+1)*(cot(Acute Angle between Diagonals of Rectangle/2)+1)). To calculate Area of Rectangle given Perimeter and Acute Angle between Diagonals, you need Perimeter of Rectangle (P) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)). With our tool, you need to enter the respective value for Perimeter of Rectangle & Acute Angle between Diagonals of Rectangle 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 Rectangle?

In this formula, Area of Rectangle uses Perimeter of Rectangle & Acute Angle between Diagonals of Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Rectangle = Breadth of Rectangle*sqrt(Diagonal of Rectangle^2-Breadth of Rectangle^2)
Area of Rectangle = ((Perimeter of Rectangle*Length of Rectangle)-(2*Length of Rectangle^2))/2
Area of Rectangle = Length of Rectangle*sqrt(Diagonal of Rectangle^2-Length of Rectangle^2)

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