Length of Rectangle given Area and Diameter of Circumcircle Calculator

✖Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.ⓘ Diameter of Circumcircle of Rectangle [D_c]			+10% -10%
✖Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.ⓘ Area of Rectangle [A]			+10% -10%

✖Length of Rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.ⓘ Length of Rectangle given Area and Diameter of Circumcircle [l]

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Formula

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Length of Rectangle given Area and Diameter of Circumcircle

Formula

l = \sqrt{\frac{{D c}^{2} + \sqrt{{D c}^{4} - (4 \cdot A^{2})}}{2}}

Example

8 m = \sqrt{\frac{{10 m}^{2} + \sqrt{{10 m}^{4} - (4 \cdot {48 m²}^{2})}}{2}}

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Length of Rectangle given Area and Diameter of Circumcircle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Rectangle = sqrt((Diameter of Circumcircle of Rectangle^2+sqrt(Diameter of Circumcircle of Rectangle^4-(4*Area of Rectangle^2)))/2)
l = sqrt((D_c^2+sqrt(D_c^4-(4*A^2)))/2)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Length of Rectangle - (Measured in Meter) - Length of Rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
Diameter of Circumcircle of Rectangle - (Measured in Meter) - Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.
Area of Rectangle - (Measured in Square Meter) - Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.

STEP 1: Convert Input(s) to Base Unit

Diameter of Circumcircle of Rectangle: 10 Meter --> 10 Meter No Conversion Required
Area of Rectangle: 48 Square Meter --> 48 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = sqrt((D_c^2+sqrt(D_c^4-(4*A^2)))/2) --> sqrt((10^2+sqrt(10^4-(4*48^2)))/2)

Evaluating ... ...

l = 8

STEP 3: Convert Result to Output's Unit

8 Meter --> No Conversion Required

FINAL ANSWER

8 Meter <-- Length of Rectangle

(Calculation completed in 00.004 seconds)

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< Length of Rectangle Calculators

Length of Rectangle given Diagonal and Obtuse Angle between Diagonals

Go Length of Rectangle = Diagonal of Rectangle*sin(Obtuse Angle between Diagonals of Rectangle/2)

Length of Rectangle given Diagonal and Breadth

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

Length of Rectangle given Perimeter and Breadth

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

Length of Rectangle given Area and Breadth

Go Length of Rectangle = Area of Rectangle/Breadth of Rectangle

Length of Rectangle given Area and Diameter of Circumcircle Formula

Length of Rectangle = sqrt((Diameter of Circumcircle of Rectangle^2+sqrt(Diameter of Circumcircle of Rectangle^4-(4*Area of Rectangle^2)))/2)
l = sqrt((D_c^2+sqrt(D_c^4-(4*A^2)))/2)

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 Length of Rectangle given Area and Diameter of Circumcircle?

Length of Rectangle given Area and Diameter of Circumcircle calculator uses Length of Rectangle = sqrt((Diameter of Circumcircle of Rectangle^2+sqrt(Diameter of Circumcircle of Rectangle^4-(4*Area of Rectangle^2)))/2) to calculate the Length of Rectangle, The Length of Rectangle given Area and Diameter of Circumcircle formula is defined as any one of the pair of parallel sides which are longer than the remaining pair of parallel sides and calculated using Area and Diameter of Circumcircle of the Rectangle. Length of Rectangle is denoted by l symbol.

How to calculate Length of Rectangle given Area and Diameter of Circumcircle using this online calculator? To use this online calculator for Length of Rectangle given Area and Diameter of Circumcircle, enter Diameter of Circumcircle of Rectangle (D_c) & Area of Rectangle (A) and hit the calculate button. Here is how the Length of Rectangle given Area and Diameter of Circumcircle calculation can be explained with given input values -> 8 = sqrt((10^2+sqrt(10^4-(4*48^2)))/2).

FAQ

What is Length of Rectangle given Area and Diameter of Circumcircle?

The Length of Rectangle given Area and Diameter of Circumcircle formula is defined as any one of the pair of parallel sides which are longer than the remaining pair of parallel sides and calculated using Area and Diameter of Circumcircle of the Rectangle and is represented as l = sqrt((D_c^2+sqrt(D_c^4-(4*A^2)))/2) or Length of Rectangle = sqrt((Diameter of Circumcircle of Rectangle^2+sqrt(Diameter of Circumcircle of Rectangle^4-(4*Area of Rectangle^2)))/2). Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle & Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.

How to calculate Length of Rectangle given Area and Diameter of Circumcircle?

The Length of Rectangle given Area and Diameter of Circumcircle formula is defined as any one of the pair of parallel sides which are longer than the remaining pair of parallel sides and calculated using Area and Diameter of Circumcircle of the Rectangle is calculated using Length of Rectangle = sqrt((Diameter of Circumcircle of Rectangle^2+sqrt(Diameter of Circumcircle of Rectangle^4-(4*Area of Rectangle^2)))/2). To calculate Length of Rectangle given Area and Diameter of Circumcircle, you need Diameter of Circumcircle of Rectangle (D_c) & Area of Rectangle (A). With our tool, you need to enter the respective value for Diameter of Circumcircle of Rectangle & Area 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 Length of Rectangle?

In this formula, Length of Rectangle uses Diameter of Circumcircle of Rectangle & Area of Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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