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Diagonal of Hexadecagon across Three Sides given Area Formula

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Diagonal across Three Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the three sides of the Hexadecagon. Check FAQs

d 3 = \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}} \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})}

d₃ - Diagonal across Three Sides of Hexadecagon?A - Area of Hexadecagon?π - Archimedes' constant?

Diagonal of Hexadecagon across Three Sides given Area Example

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Here is how the Diagonal of Hexadecagon across Three Sides given Area equation looks like with Values.

Here is how the Diagonal of Hexadecagon across Three Sides given Area equation looks like with Units.

Here is how the Diagonal of Hexadecagon across Three Sides given Area equation looks like.

14.2 = \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}} \cdot \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})}

14.2m = \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}} \cdot \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})}

14.2 = \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}} \cdot \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})}

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Diagonal of Hexadecagon across Three Sides given Area Solution

Follow our step by step solution on how to calculate Diagonal of Hexadecagon across Three Sides given Area?

FIRST Step Consider the formula

d 3 = \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}} \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})}

Next Step Substitute values of Variables

∴

d 3 = \sqrt{\frac{500m²}{4 \cdot \cot (\frac{π}{16})}} \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})}

Next Step Substitute values of Constants

∴

d 3 = \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}} \cdot \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})}

Next Step Prepare to Evaluate

∴

d 3 = \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}} \cdot \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})}

Next Step Evaluate

∴

d 3 = 14.2000260992399m

LAST Step Rounding Answer

∴

d 3 = 14.2m

Diagonal of Hexadecagon across Three Sides given Area Formula Elements

Variables

Constants

Functions

Diagonal across Three Sides of Hexadecagon

Diagonal across Three Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the three sides of the Hexadecagon.

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Three Sides of Hexadecagon

Area of Hexadecagon

Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Hexadecagon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

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.

Syntax: sqrt(Number)

Other Formulas to find Diagonal across Three Sides of Hexadecagon

Go Diagonal of Hexadecagon across Three Sides

d 3 = \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot S

Go Diagonal of Hexadecagon across Three Sides given Height

d 3 = h \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{7 \cdot π}{16})}

Go Diagonal of Hexadecagon across Three Sides given Perimeter

d 3 = \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{P}{16}

Go Diagonal of Hexadecagon across Three Sides given Circumradius

d 3 = \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

How to Evaluate Diagonal of Hexadecagon across Three Sides given Area?

Diagonal of Hexadecagon across Three Sides given Area evaluator uses Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16) to evaluate the Diagonal across Three Sides of Hexadecagon, Diagonal of Hexadecagon across Three Sides given Area formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the area. Diagonal across Three Sides of Hexadecagon is denoted by d₃ symbol.

How to evaluate Diagonal of Hexadecagon across Three Sides given Area using this online evaluator? To use this online evaluator for Diagonal of Hexadecagon across Three Sides given Area, enter Area of Hexadecagon (A) and hit the calculate button.

FAQs on Diagonal of Hexadecagon across Three Sides given Area

What is the formula to find Diagonal of Hexadecagon across Three Sides given Area?

The formula of Diagonal of Hexadecagon across Three Sides given Area is expressed as Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16). Here is an example- 14.20003 = sqrt(500/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16).

How to calculate Diagonal of Hexadecagon across Three Sides given Area?

With Area of Hexadecagon (A) we can find Diagonal of Hexadecagon across Three Sides given Area using the formula - Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16). This formula also uses Archimedes' constant and , Sine (sin), Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal across Three Sides of Hexadecagon?

Here are the different ways to Calculate Diagonal across Three Sides of Hexadecagon-

Diagonal across Three Sides of Hexadecagon=sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Three Sides of Hexadecagon=Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)
Diagonal across Three Sides of Hexadecagon=sin((3*pi)/16)/sin(pi/16)*Perimeter of Hexadecagon/16

Can the Diagonal of Hexadecagon across Three Sides given Area be negative?

No, the Diagonal of Hexadecagon across Three Sides given Area, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Hexadecagon across Three Sides given Area?

Diagonal of Hexadecagon across Three Sides given Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diagonal of Hexadecagon across Three Sides given Area can be measured.

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