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Inradius of Pentagon given Area using Interior Angle Formula

GoInradius of Pentagon given Edge Length using Central Angle Formula

GoInradius of Pentagon given Circumradius using Central Angle Formula

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

r i = \sqrt{\frac{2 \cdot A \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot π)}}

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

Inradius of Pentagon given Area using Interior Angle Example

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Here is how the Inradius of Pentagon given Area using Interior Angle equation looks like with Values.

Here is how the Inradius of Pentagon given Area using Interior Angle equation looks like with Units.

Here is how the Inradius of Pentagon given Area using Interior Angle equation looks like.

6.8408 = \sqrt{\frac{2 \cdot 170 \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot 3.1416)}}

6.8408m = \sqrt{\frac{2 \cdot 170m² \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot 3.1416)}}

6.8408 = \sqrt{\frac{2 \cdot 170 \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot 3.1416)}}

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Inradius of Pentagon given Area using Interior Angle Solution

Follow our step by step solution on how to calculate Inradius of Pentagon given Area using Interior Angle?

FIRST Step Consider the formula

r i = \sqrt{\frac{2 \cdot A \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot π)}}

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{2 \cdot 170m² \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot π)}}

Next Step Substitute values of Constants

∴

r i = \sqrt{\frac{2 \cdot 170m² \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot 3.1416)}}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{2 \cdot 170 \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{5 \cdot \sin (\frac{3}{5} \cdot 3.1416)}}

Next Step Evaluate

∴

r i = 6.84083220785453m

LAST Step Rounding Answer

∴

r i = 6.8408m

Inradius of Pentagon given Area using Interior Angle Formula Elements

Variables

Constants

Functions

Inradius of Pentagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

Area of Pentagon

The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Pentagon

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(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 Pentagon

Go Inradius of Pentagon given Edge Length using Central Angle

r i = \frac{l e}{2 \cdot \tan (\frac{π}{5})}

Go Inradius of Pentagon given Circumradius using Central Angle

r i = r c \cdot \cos (\frac{π}{5})

Go Inradius of Pentagon given Circumradius

r i = \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}} \cdot r c

Go Inradius of Pentagon given Height using Central Angle

r i = \frac{h}{1 + (\frac{1}{\cos (\frac{π}{5})})}

How to Evaluate Inradius of Pentagon given Area using Interior Angle?

Inradius of Pentagon given Area using Interior Angle evaluator uses Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi))) to evaluate the Inradius of Pentagon, The Inradius of Pentagon given Area using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using area and interior angle. Inradius of Pentagon is denoted by r_i symbol.

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

FAQs on Inradius of Pentagon given Area using Interior Angle

What is the formula to find Inradius of Pentagon given Area using Interior Angle?

The formula of Inradius of Pentagon given Area using Interior Angle is expressed as Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi))). Here is an example- 6.840832 = sqrt((2*170*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi))).

How to calculate Inradius of Pentagon given Area using Interior Angle?

With Area of Pentagon (A) we can find Inradius of Pentagon given Area using Interior Angle using the formula - Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Pentagon?

Here are the different ways to Calculate Inradius of Pentagon-

Inradius of Pentagon=(Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon=Circumradius of Pentagon*cos(pi/5)
Inradius of Pentagon=sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Can the Inradius of Pentagon given Area using Interior Angle be negative?

No, the Inradius of Pentagon given Area using Interior Angle, measured in Length cannot be negative.

Which unit is used to measure Inradius of Pentagon given Area using Interior Angle?

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

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