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Area of Golden Rectangle given diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi]
A = ((sqrt((d^2)/((1+(1/[phi]^2)))))^2)/[phi]
This formula uses 1 Constants, 1 Functions, 1 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Diagonal - A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Diagonal: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = ((sqrt((d^2)/((1+(1/[phi]^2)))))^2)/[phi] --> ((sqrt((8^2)/((1+(1/[phi]^2)))))^2)/[phi]
Evaluating ... ...
A = 28.6216701119973
STEP 3: Convert Result to Output's Unit
28.6216701119973 Square Meter --> No Conversion Required
FINAL ANSWER
28.6216701119973 Square Meter <-- Area
(Calculation completed in 00.015 seconds)

4 Area of Golden Rectangle Calculators

Area of Golden Rectangle given diagonal
area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi] Go
Area of Golden Rectangle given perimeter
area = ((Perimeter/(2*(1+(1/[phi]))))^2)/[phi] Go
Area of Golden Rectangle given short side
area = ((Short edge*[phi])^2)/[phi] Go
Area of Golden Rectangle
area = (Long edge^2)/[phi] Go

Area of Golden Rectangle given diagonal Formula

area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi]
A = ((sqrt((d^2)/((1+(1/[phi]^2)))))^2)/[phi]

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 = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi] to calculate the Area, The Area of golden rectangle given diagonal formula is defined as measure of the total area that the surface of the object occupies of a golden rectangle , where area = area of golden rectangle. Area and 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 (d) and hit the calculate button. Here is how the Area of Golden Rectangle given diagonal calculation can be explained with given input values -> 28.62167 = ((sqrt((8^2)/((1+(1/[phi]^2)))))^2)/[phi].

FAQ

What is Area of Golden Rectangle given diagonal?
The Area of golden rectangle given diagonal formula is defined as measure of the total area that the surface of the object occupies of a golden rectangle , where area = area of golden rectangle and is represented as A = ((sqrt((d^2)/((1+(1/[phi]^2)))))^2)/[phi] or area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi]. A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape.
How to calculate Area of Golden Rectangle given diagonal?
The Area of golden rectangle given diagonal formula is defined as measure of the total area that the surface of the object occupies of a golden rectangle , where area = area of golden rectangle is calculated using area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi]. To calculate Area of Golden Rectangle given diagonal, you need Diagonal (d). With our tool, you need to enter the respective value for Diagonal 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?
In this formula, Area uses Diagonal. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • area = (Long edge^2)/[phi]
  • area = ((Short edge*[phi])^2)/[phi]
  • area = ((sqrt((Diagonal^2)/((1+(1/[phi]^2)))))^2)/[phi]
  • area = ((Perimeter/(2*(1+(1/[phi]))))^2)/[phi]
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