Area of Rectangle given Circumradius and Acute Angle between Diagonals Calculator

✖Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.ⓘ Circumradius of Rectangle [r_c]			+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 Circumradius and Acute Angle between Diagonals [A]

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Area of Rectangle given Circumradius and Acute Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Rectangle = 4*Circumradius of Rectangle^2*cos(Acute Angle between Diagonals of Rectangle/2)*sin(Acute Angle between Diagonals of Rectangle/2)
A = 4*r_c^2*cos(∠_d(Acute)/2)*sin(∠_d(Acute)/2)
This formula uses 2 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)
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

Area of Rectangle - (Measured in Square Meter) - Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.
Circumradius of Rectangle - (Measured in Meter) - Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.
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

Circumradius of Rectangle: 5 Meter --> 5 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 = 4*r_c^2*cos(∠_d(Acute)/2)*sin(∠_d(Acute)/2) --> 4*5^2*cos(1.2217304763958/2)*sin(1.2217304763958/2)

Evaluating ... ...

A = 46.9846310392915

STEP 3: Convert Result to Output's Unit

46.9846310392915 Square Meter --> No Conversion Required

FINAL ANSWER

46.9846310392915 ≈ 46.98463 Square Meter <-- Area of Rectangle

(Calculation completed in 00.020 seconds)

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Created by Yashika Gupta

Indian Institute of Technology Mandi (IIT Mandi), Himachal pradesh

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< Area of Rectangle Calculators

Area of Rectangle given Breadth and Diagonal

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

Area of Rectangle given Length and Diagonal

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

Area of Rectangle given Perimeter and Length

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

Area of Rectangle

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

Area of Rectangle given Circumradius and Acute Angle between Diagonals Formula

LaTeX Go

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 Circumradius and Acute Angle between Diagonals?

Area of Rectangle given Circumradius and Acute Angle between Diagonals calculator 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 calculate 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 calculate Area of Rectangle given Circumradius and Acute Angle between Diagonals using this online calculator? To use this online calculator 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. Here is how the Area of Rectangle given Circumradius and Acute Angle between Diagonals calculation can be explained with given input values -> 46.98463 = 4*5^2*cos(1.2217304763958/2)*sin(1.2217304763958/2).

FAQ

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

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 and is represented as A = 4*r_c^2*cos(∠_d(Acute)/2)*sin(∠_d(Acute)/2) or Area of Rectangle = 4*Circumradius of Rectangle^2*cos(Acute Angle between Diagonals of Rectangle/2)*sin(Acute Angle between Diagonals of Rectangle/2). Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle & 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 Circumradius and Acute Angle between Diagonals?

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 is calculated using 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 calculate Area of Rectangle given Circumradius and Acute Angle between Diagonals, you need Circumradius of Rectangle (r_c) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)). With our tool, you need to enter the respective value for Circumradius 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 Circumradius 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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