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Inradius of Hexadecagon given Area Formula

GoInradius of Hexadecagon Formula

GoInradius of Hexadecagon given Diagonal across Seven Sides Formula

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Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon. Check FAQs

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}}

r_i - Inradius of Hexadecagon?A - Area of Hexadecagon?π - Archimedes' constant?

Inradius of Hexadecagon given Area Example

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Here is how the Inradius of Hexadecagon given Area equation looks like.

12.5341 = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

12.5341m = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}}

12.5341 = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

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Inradius of Hexadecagon given Area Solution

Follow our step by step solution on how to calculate Inradius of Hexadecagon given Area?

FIRST Step Consider the formula

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}}

Next Step Substitute values of Variables

∴

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{π}{16})}}

Next Step Substitute values of Constants

∴

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}}

Next Step Prepare to Evaluate

∴

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

Next Step Evaluate

∴

r i = 12.5341277769509m

LAST Step Rounding Answer

∴

r i = 12.5341m

Inradius of Hexadecagon given Area Formula Elements

Variables

Constants

Functions

Inradius of Hexadecagon

Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius 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

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 Inradius of Hexadecagon

Go Inradius of Hexadecagon

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot S

Go Inradius of Hexadecagon given Diagonal across Seven Sides

r i = \frac{d 7}{2}

Go Inradius of Hexadecagon given Diagonal across Eight Sides

r i = d 8 \cdot \sin (\frac{π}{16}) \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Go Inradius of Hexadecagon given Diagonal across Six Sides

r i = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

How to Evaluate Inradius of Hexadecagon given Area?

Inradius of Hexadecagon given Area evaluator uses Inradius of Hexadecagon = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))) to evaluate the Inradius of Hexadecagon, The Inradius of Hexadecagon given Area formula is defined as a straight line connecting in-center and any point on circle that touches all sides of the Hexadecagon, calculated using area. Inradius of Hexadecagon is denoted by r_i symbol.

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

FAQs on Inradius of Hexadecagon given Area

What is the formula to find Inradius of Hexadecagon given Area?

The formula of Inradius of Hexadecagon given Area is expressed as Inradius of Hexadecagon = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))). Here is an example- 12.53413 = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*sqrt((500)/(4*cot(pi/16))).

How to calculate Inradius of Hexadecagon given Area?

With Area of Hexadecagon (A) we can find Inradius of Hexadecagon given Area using the formula - Inradius of Hexadecagon = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))). This formula also uses Archimedes' constant and , Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Hexadecagon?

Here are the different ways to Calculate Inradius of Hexadecagon-

Inradius of Hexadecagon=((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*Side of Hexadecagon
Inradius of Hexadecagon=Diagonal across Seven Sides of Hexadecagon/2
Inradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

Can the Inradius of Hexadecagon given Area be negative?

No, the Inradius of Hexadecagon given Area, measured in Length cannot be negative.

Which unit is used to measure Inradius of Hexadecagon given Area?

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

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