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Edge Length of Pentagon given Inradius using Interior Angle Formula

GoEdge Length of Pentagon given Area and Inradius Formula

GoEdge Length of Pentagon given Height using Central Angle Formula

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The Edge Length of Pentagon is the length of one of the five sides of the Pentagon. Check FAQs

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

l_e - Edge Length of Pentagon?r_i - Inradius of Pentagon?π - Archimedes' constant?

Edge Length of Pentagon given Inradius using Interior Angle Example

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

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

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

10.1716 = 7 \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

10.1716m = 7m \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

10.1716 = 7 \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

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Edge Length of Pentagon given Inradius using Interior Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l e = 7m \cdot \frac{\sin (\frac{3}{5} \cdot π)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}

Next Step Substitute values of Constants

∴

l e = 7m \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

Next Step Prepare to Evaluate

∴

l e = 7 \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

Next Step Evaluate

∴

l e = 10.1715953920751m

LAST Step Rounding Answer

∴

l e = 10.1716m

Edge Length of Pentagon given Inradius using Interior Angle Formula Elements

Variables

Constants

Functions

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Pentagon

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

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)

Other Formulas to find Edge Length of Pentagon

Go Edge Length of Pentagon given Area and Inradius

l e = \frac{2 \cdot A}{5 \cdot r i}

Go Edge Length of Pentagon given Height using Central Angle

l e = \frac{2 \cdot h \cdot \sin (\frac{π}{5})}{1 + \cos (\frac{π}{5})}

Go Edge Length of Pentagon given Inradius

l e = r i \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Go Edge Length of Pentagon given Area

l e = \sqrt{4 \cdot \frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Edge Length of Pentagon given Inradius using Interior Angle?

Edge Length of Pentagon given Inradius using Interior Angle evaluator uses Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 to evaluate the Edge Length of Pentagon, The Edge Length of Pentagon given Inradius using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and interior angle. Edge Length of Pentagon is denoted by l_e symbol.

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

FAQs on Edge Length of Pentagon given Inradius using Interior Angle

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

The formula of Edge Length of Pentagon given Inradius using Interior Angle is expressed as Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. Here is an example- 10.1716 = 7*sin(3/5*pi)/(1/2-cos(3/5*pi))^2.

How to calculate Edge Length of Pentagon given Inradius using Interior Angle?

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

What are the other ways to Calculate Edge Length of Pentagon?

Here are the different ways to Calculate Edge Length of Pentagon-

Edge Length of Pentagon=(2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon=(2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon=Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))

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

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

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

Edge Length of Pentagon given Inradius 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 Edge Length of Pentagon given Inradius using Interior Angle can be measured.

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