Area of Golden Rectangle given Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2
A = [phi]/(1+[phi]^2)*d^2
This formula uses 1 Constants, 2 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
Variables Used
Area of Golden Rectangle - (Measured in Square Meter) - The Area of Golden Rectangle is the total quantity of plane enclosed by the boundary of Golden Rectangle.
Diagonal of Golden Rectangle - (Measured in Meter) - The Diagonal of Golden Rectangle is the distance between any pair of opposite vertices of Golden Rectangle.
STEP 1: Convert Input(s) to Base Unit
Diagonal of Golden Rectangle: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = [phi]/(1+[phi]^2)*d^2 --> [phi]/(1+[phi]^2)*12^2
Evaluating ... ...
A = 64.3987577519939
STEP 3: Convert Result to Output's Unit
64.3987577519939 Square Meter --> No Conversion Required
FINAL ANSWER
64.3987577519939 64.39876 Square Meter <-- Area of Golden Rectangle
(Calculation completed in 00.020 seconds)

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4 Area of Golden Rectangle Calculators

Area of Golden Rectangle given Perimeter
Go Area of Golden Rectangle = [phi]*(Perimeter of Golden Rectangle/(2*(1+[phi])))^2
Area of Golden Rectangle given Diagonal
Go Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2
Area of Golden Rectangle
Go Area of Golden Rectangle = (Length of Golden Rectangle^2)/[phi]
Area of Golden Rectangle given Breadth
Go Area of Golden Rectangle = [phi]*Breadth of Golden Rectangle^2

Area of Golden Rectangle given Diagonal Formula

Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2
A = [phi]/(1+[phi]^2)*d^2

What is a Golden Rectangle?

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:1+sqrt(5)/2 which is 1:phi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. Diagonal lines drawn between the first two orders of embedded golden rectangles will define the intersection point of the diagonals of all the embedded golden rectangles; Clifford A. Pickover referred to this point as "the Eye of God"

How to Calculate Area of Golden Rectangle given Diagonal?

Area of Golden Rectangle given Diagonal calculator uses Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2 to calculate the Area of Golden Rectangle, The Area of Golden Rectangle given Diagonal formula is defined as the total quantity of plane enclosed by the boundary of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle. Area of Golden Rectangle is denoted by A symbol.

How to calculate Area of Golden Rectangle given Diagonal using this online calculator? To use this online calculator for Area of Golden Rectangle given Diagonal, enter Diagonal of Golden Rectangle (d) and hit the calculate button. Here is how the Area of Golden Rectangle given Diagonal calculation can be explained with given input values -> 64.39876 = [phi]/(1+[phi]^2)*12^2.

FAQ

What is Area of Golden Rectangle given Diagonal?
The Area of Golden Rectangle given Diagonal formula is defined as the total quantity of plane enclosed by the boundary of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle and is represented as A = [phi]/(1+[phi]^2)*d^2 or Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2. The Diagonal of Golden Rectangle is the distance between any pair of opposite vertices of Golden Rectangle.
How to calculate Area of Golden Rectangle given Diagonal?
The Area of Golden Rectangle given Diagonal formula is defined as the total quantity of plane enclosed by the boundary of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle is calculated using Area of Golden Rectangle = [phi]/(1+[phi]^2)*Diagonal of Golden Rectangle^2. To calculate Area of Golden Rectangle given Diagonal, you need Diagonal of Golden Rectangle (d). With our tool, you need to enter the respective value for Diagonal of Golden 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 Golden Rectangle?
In this formula, Area of Golden Rectangle uses Diagonal of Golden Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Area of Golden Rectangle = (Length of Golden Rectangle^2)/[phi]
  • Area of Golden Rectangle = [phi]*Breadth of Golden Rectangle^2
  • Area of Golden Rectangle = [phi]*(Perimeter of Golden Rectangle/(2*(1+[phi])))^2
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