Long Diagonal of Hexagon given Area of Equilateral Triangle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3)))
dLong = sqrt((48*AEquilateral Triangle)/(3*sqrt(3)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Long Diagonal of Hexagon - (Measured in Meter) - The Long Diagonal of Hexagon is the length of the line joining any pair of opposite vertices of the Hexagon.
Area of Equilateral Triangle of Hexagon - (Measured in Square Meter) - Area of Equilateral Triangle of Hexagon is defined as the area of each of the Equilateral triangles, forming the Hexagon.
STEP 1: Convert Input(s) to Base Unit
Area of Equilateral Triangle of Hexagon: 15 Square Meter --> 15 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dLong = sqrt((48*AEquilateral Triangle)/(3*sqrt(3))) --> sqrt((48*15)/(3*sqrt(3)))
Evaluating ... ...
dLong = 11.7713238255308
STEP 3: Convert Result to Output's Unit
11.7713238255308 Meter --> No Conversion Required
FINAL ANSWER
11.7713238255308 Meter <-- Long Diagonal of Hexagon
(Calculation completed in 00.009 seconds)

Credits

Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
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9 Long Diagonal of Hexagon Calculators

Long Diagonal of Hexagon given Area of Equilateral Triangle
Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3))) Go
Long Diagonal of Hexagon given Area
Long Diagonal of Hexagon = sqrt((8*Area of Hexagon)/(3*sqrt(3))) Go
Long Diagonal of Hexagon given Short Diagonal
Long Diagonal of Hexagon = (2/sqrt(3))*Short Diagonal of Hexagon Go
Long Diagonal of Hexagon given Inradius
Long Diagonal of Hexagon = (4/sqrt(3))*Inradius of Hexagon Go
Long Diagonal of Hexagon given Height
Long Diagonal of Hexagon = (2/sqrt(3))*Height of Hexagon Go
Long Diagonal of Hexagon given Circumradius
Long Diagonal of Hexagon = 2*Circumradius of Hexagon Go
Long Diagonal of Hexagon
Long Diagonal of Hexagon = 2*Edge Length of Hexagon Go
Long Diagonal of Hexagon given Perimeter
Long Diagonal of Hexagon = Perimeter of Hexagon/3 Go
Long Diagonal of Hexagon given Width
Long Diagonal of Hexagon = Width of Hexagon/1 Go

Long Diagonal of Hexagon given Area of Equilateral Triangle Formula

Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3)))
dLong = sqrt((48*AEquilateral Triangle)/(3*sqrt(3)))

What is Hexagon?

A regular Hexagon is defined as a hexagon that is both equilateral and equiangular. Simply it is the six sided regular polygon. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals 2/sqrt(3) times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular Hexagon has six rotational symmetries.

How to Calculate Long Diagonal of Hexagon given Area of Equilateral Triangle?

Long Diagonal of Hexagon given Area of Equilateral Triangle calculator uses Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3))) to calculate the Long Diagonal of Hexagon, The Long Diagonal of Hexagon given Area of Equilateral Triangle formula is defined as the length of the line joining any pair of opposite vertices of the Regular Hexagon, calculated using the area of an equilateral triangle of Hexagon. Long Diagonal of Hexagon is denoted by dLong symbol.

How to calculate Long Diagonal of Hexagon given Area of Equilateral Triangle using this online calculator? To use this online calculator for Long Diagonal of Hexagon given Area of Equilateral Triangle, enter Area of Equilateral Triangle of Hexagon (AEquilateral Triangle) and hit the calculate button. Here is how the Long Diagonal of Hexagon given Area of Equilateral Triangle calculation can be explained with given input values -> 11.77132 = sqrt((48*15)/(3*sqrt(3))).

FAQ

What is Long Diagonal of Hexagon given Area of Equilateral Triangle?
The Long Diagonal of Hexagon given Area of Equilateral Triangle formula is defined as the length of the line joining any pair of opposite vertices of the Regular Hexagon, calculated using the area of an equilateral triangle of Hexagon and is represented as dLong = sqrt((48*AEquilateral Triangle)/(3*sqrt(3))) or Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3))). Area of Equilateral Triangle of Hexagon is defined as the area of each of the Equilateral triangles, forming the Hexagon.
How to calculate Long Diagonal of Hexagon given Area of Equilateral Triangle?
The Long Diagonal of Hexagon given Area of Equilateral Triangle formula is defined as the length of the line joining any pair of opposite vertices of the Regular Hexagon, calculated using the area of an equilateral triangle of Hexagon is calculated using Long Diagonal of Hexagon = sqrt((48*Area of Equilateral Triangle of Hexagon)/(3*sqrt(3))). To calculate Long Diagonal of Hexagon given Area of Equilateral Triangle, you need Area of Equilateral Triangle of Hexagon (AEquilateral Triangle). With our tool, you need to enter the respective value for Area of Equilateral Triangle of Hexagon 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 Long Diagonal of Hexagon?
In this formula, Long Diagonal of Hexagon uses Area of Equilateral Triangle of Hexagon. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Long Diagonal of Hexagon = (2/sqrt(3))*Height of Hexagon
  • Long Diagonal of Hexagon = (4/sqrt(3))*Inradius of Hexagon
  • Long Diagonal of Hexagon = Perimeter of Hexagon/3
  • Long Diagonal of Hexagon = (2/sqrt(3))*Short Diagonal of Hexagon
  • Long Diagonal of Hexagon = sqrt((8*Area of Hexagon)/(3*sqrt(3)))
  • Long Diagonal of Hexagon = 2*Edge Length of Hexagon
  • Long Diagonal of Hexagon = 2*Circumradius of Hexagon
  • Long Diagonal of Hexagon = Width of Hexagon/1
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