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Area of Rectangle given Circumradius and Acute Angle between Diagonals 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 = 4 \cdot {r c}^{2} \cdot \cos (\frac{∠ d(Acute)}{2}) \cdot \sin (\frac{∠ d(Acute)}{2})

A - Area of Rectangle?r_c - Circumradius of Rectangle?∠_d(Acute) - Acute Angle between Diagonals of Rectangle?

Area of Rectangle given Circumradius and Acute Angle between Diagonals Example

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Here is how the Area of Rectangle given Circumradius and Acute Angle between Diagonals equation looks like with Values.

Here is how the Area of Rectangle given Circumradius and Acute Angle between Diagonals equation looks like with Units.

Here is how the Area of Rectangle given Circumradius and Acute Angle between Diagonals equation looks like.

46.9846 = 4 \cdot 5^{2} \cdot \cos (\frac{70}{2}) \cdot \sin (\frac{70}{2})

46.9846m² = 4 \cdot {5m}^{2} \cdot \cos (\frac{70°}{2}) \cdot \sin (\frac{70°}{2})

46.9846 = 4 \cdot 5^{2} \cdot \cos (\frac{70}{2}) \cdot \sin (\frac{70}{2})

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Area of Rectangle given Circumradius and Acute Angle between Diagonals Solution

Follow our step by step solution on how to calculate Area of Rectangle given Circumradius and Acute Angle between Diagonals?

FIRST Step Consider the formula

A = 4 \cdot {r c}^{2} \cdot \cos (\frac{∠ d(Acute)}{2}) \cdot \sin (\frac{∠ d(Acute)}{2})

Next Step Substitute values of Variables

∴

A = 4 \cdot {5m}^{2} \cdot \cos (\frac{70°}{2}) \cdot \sin (\frac{70°}{2})

Next Step Convert Units

∴

A = 4 \cdot {5m}^{2} \cdot \cos (\frac{1.2217rad}{2}) \cdot \sin (\frac{1.2217rad}{2})

Next Step Prepare to Evaluate

∴

A = 4 \cdot 5^{2} \cdot \cos (\frac{1.2217}{2}) \cdot \sin (\frac{1.2217}{2})

Next Step Evaluate

∴

A = 46.9846310392915m²

LAST Step Rounding Answer

∴

A = 46.9846m²

Area of Rectangle given Circumradius and Acute Angle between Diagonals 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

Circumradius of Rectangle

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Rectangle

Acute Angle between Diagonals of Rectangle

Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.

Symbol: ∠_d(Acute)

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle between Diagonals 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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(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 Circumradius and Acute Angle between Diagonals?

Area of Rectangle given Circumradius and Acute Angle between Diagonals evaluator uses Area of Rectangle = 4*Circumradius of Rectangle^2*cos(Acute Angle between Diagonals of Rectangle/2)*sin(Acute Angle between Diagonals of Rectangle/2) to evaluate the Area of Rectangle, The Area of Rectangle given Circumradius and Acute Angle between Diagonals formula is defined as the total quantity of plane enclosed by the boundary of the Rectangle, and calculated using circumradius and acute angle between diagonals of the Rectangle. Area of Rectangle is denoted by A symbol.

How to evaluate Area of Rectangle given Circumradius and Acute Angle between Diagonals using this online evaluator? To use this online evaluator for Area of Rectangle given Circumradius and Acute Angle between Diagonals, enter Circumradius of Rectangle (r_c) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) and hit the calculate button.

FAQs on Area of Rectangle given Circumradius and Acute Angle between Diagonals

What is the formula to find Area of Rectangle given Circumradius and Acute Angle between Diagonals?

The formula of Area of Rectangle given Circumradius and Acute Angle between Diagonals is expressed as Area of Rectangle = 4*Circumradius of Rectangle^2*cos(Acute Angle between Diagonals of Rectangle/2)*sin(Acute Angle between Diagonals of Rectangle/2). Here is an example- 46.98463 = 4*5^2*cos(1.2217304763958/2)*sin(1.2217304763958/2).

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

With Circumradius of Rectangle (r_c) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) we can find Area of Rectangle given Circumradius and Acute Angle between Diagonals using the formula - Area of Rectangle = 4*Circumradius of Rectangle^2*cos(Acute Angle between Diagonals of Rectangle/2)*sin(Acute Angle between Diagonals of Rectangle/2). This formula also uses Sine, Cosine 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 Circumradius and Acute Angle between Diagonals be negative?

No, the Area of Rectangle given Circumradius and Acute Angle between Diagonals, measured in Area cannot be negative.

Which unit is used to measure Area of Rectangle given Circumradius and Acute Angle between Diagonals?

Area of Rectangle given Circumradius and Acute Angle between Diagonals 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 Circumradius and Acute Angle between Diagonals can be measured.

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