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Area of Rectangle given Diagonal and Angle between Diagonal and Length Formula

GoArea of Rectangle given Breadth and Diagonal Formula

GoArea of Rectangle given Perimeter and Length Formula

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Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle. Check FAQs

A = \frac{d^{2} \cdot \sin (2 \cdot ∠ dl)}{2}

A - Area of Rectangle?d - Diagonal of Rectangle?∠_dl - Angle between Diagonal and Length of Rectangle?

Area of Rectangle given Diagonal and Angle between Diagonal and Length Example

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Here is how the Area of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like with Values.

Here is how the Area of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like with Units.

Here is how the Area of Rectangle given Diagonal and Angle between Diagonal and Length equation looks like.

46.9846 = \frac{10^{2} \cdot \sin (2 \cdot 35)}{2}

46.9846m² = \frac{{10m}^{2} \cdot \sin (2 \cdot 35°)}{2}

46.9846 = \frac{10^{2} \cdot \sin (2 \cdot 35)}{2}

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Area of Rectangle given Diagonal and Angle between Diagonal and Length Solution

Follow our step by step solution on how to calculate Area of Rectangle given Diagonal and Angle between Diagonal and Length?

FIRST Step Consider the formula

A = \frac{d^{2} \cdot \sin (2 \cdot ∠ dl)}{2}

Next Step Substitute values of Variables

∴

A = \frac{{10m}^{2} \cdot \sin (2 \cdot 35°)}{2}

Next Step Convert Units

∴

A = \frac{{10m}^{2} \cdot \sin (2 \cdot 0.6109rad)}{2}

Next Step Prepare to Evaluate

∴

A = \frac{10^{2} \cdot \sin (2 \cdot 0.6109)}{2}

Next Step Evaluate

∴

A = 46.9846310392915m²

LAST Step Rounding Answer

∴

A = 46.9846m²

Area of Rectangle given Diagonal and Angle between Diagonal and Length Formula Elements

Variables

Functions

Area of Rectangle

Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Rectangle

Diagonal of Rectangle

Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Rectangle

Angle between Diagonal and Length of Rectangle

Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.

Symbol: ∠_dl

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle between Diagonal and Length of Rectangle

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.

Syntax: sin(Angle)

Other Formulas to find Area of Rectangle

Go Area of Rectangle given Breadth and Diagonal

A = b \cdot \sqrt{d^{2} - b^{2}}

Go Area of Rectangle given Perimeter and Length

A = \frac{(P \cdot l) - (2 \cdot l^{2})}{2}

Go Area of Rectangle given Length and Diagonal

A = l \cdot \sqrt{d^{2} - l^{2}}

Go Area of Rectangle

A = l \cdot b

How to Evaluate Area of Rectangle given Diagonal and Angle between Diagonal and Length?

Area of Rectangle given Diagonal and Angle between Diagonal and Length evaluator uses Area of Rectangle = (Diagonal of Rectangle^2*sin(2*Angle between Diagonal and Length of Rectangle))/2 to evaluate the Area of Rectangle, The Area of Rectangle given Diagonal and Angle between Diagonal and Length formula is defined as the total quantity of plane enclosed by the boundary of the Rectangle, and calculated using diagonal and Angle between Diagonal and Length of the Rectangle. Area of Rectangle is denoted by A symbol.

How to evaluate Area of Rectangle given Diagonal and Angle between Diagonal and Length using this online evaluator? To use this online evaluator for Area of Rectangle given Diagonal and Angle between Diagonal and Length, enter Diagonal of Rectangle (d) & Angle between Diagonal and Length of Rectangle (∠_dl) and hit the calculate button.

FAQs on Area of Rectangle given Diagonal and Angle between Diagonal and Length

What is the formula to find Area of Rectangle given Diagonal and Angle between Diagonal and Length?

The formula of Area of Rectangle given Diagonal and Angle between Diagonal and Length is expressed as Area of Rectangle = (Diagonal of Rectangle^2*sin(2*Angle between Diagonal and Length of Rectangle))/2. Here is an example- 46.98463 = (10^2*sin(2*0.610865238197901))/2.

How to calculate Area of Rectangle given Diagonal and Angle between Diagonal and Length?

With Diagonal of Rectangle (d) & Angle between Diagonal and Length of Rectangle (∠_dl) we can find Area of Rectangle given Diagonal and Angle between Diagonal and Length using the formula - Area of Rectangle = (Diagonal of Rectangle^2*sin(2*Angle between Diagonal and Length of Rectangle))/2. This formula also uses Sine function(s).

What are the other ways to Calculate Area of Rectangle?

Here are the different ways to Calculate Area of Rectangle-

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)

Can the Area of Rectangle given Diagonal and Angle between Diagonal and Length be negative?

No, the Area of Rectangle given Diagonal and Angle between Diagonal and Length, measured in Area cannot be negative.

Which unit is used to measure Area of Rectangle given Diagonal and Angle between Diagonal and Length?

Area of Rectangle given Diagonal and Angle between Diagonal and Length is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Rectangle given Diagonal and Angle between Diagonal and Length can be measured.

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