Inradius of Pentagon given Diagonal Calculator

✖Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.ⓘ Diagonal of Pentagon [d]

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✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon given Diagonal [r_i]

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Inradius of Pentagon given Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5)))
r_i = sqrt(25+(10*sqrt(5)))*d/(5*(1+sqrt(5)))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.
Diagonal of Pentagon - (Measured in Meter) - Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal of Pentagon: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt(25+(10*sqrt(5)))*d/(5*(1+sqrt(5))) --> sqrt(25+(10*sqrt(5)))*16/(5*(1+sqrt(5)))

Evaluating ... ...

r_i = 6.80520646681632

STEP 3: Convert Result to Output's Unit

6.80520646681632 Meter --> No Conversion Required

FINAL ANSWER

6.80520646681632 ≈ 6.805206 Meter <-- Inradius of Pentagon

(Calculation completed in 00.004 seconds)

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< Inradius of Pentagon Calculators

Inradius of Pentagon given Circumradius

LaTeX Go Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Inradius of Pentagon given Edge Length using Central Angle

LaTeX Go Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))

Inradius of Pentagon given Height using Central Angle

LaTeX Go Inradius of Pentagon = (Height of Pentagon)/(1+(1/cos(pi/5)))

Inradius of Pentagon given Circumradius using Central Angle

LaTeX Go Inradius of Pentagon = Circumradius of Pentagon*cos(pi/5)

Inradius of Pentagon given Diagonal Formula

LaTeX Go

Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5)))
r_i = sqrt(25+(10*sqrt(5)))*d/(5*(1+sqrt(5)))

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

How to Calculate Inradius of Pentagon given Diagonal?

Inradius of Pentagon given Diagonal calculator uses Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))) to calculate the Inradius of Pentagon, The Inradius of Pentagon given Diagonal formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using diagonal of Pentagon. Inradius of Pentagon is denoted by r_i symbol.

How to calculate Inradius of Pentagon given Diagonal using this online calculator? To use this online calculator for Inradius of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button. Here is how the Inradius of Pentagon given Diagonal calculation can be explained with given input values -> 6.805206 = sqrt(25+(10*sqrt(5)))*16/(5*(1+sqrt(5))).

FAQ

What is Inradius of Pentagon given Diagonal?

The Inradius of Pentagon given Diagonal formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using diagonal of Pentagon and is represented as r_i = sqrt(25+(10*sqrt(5)))*d/(5*(1+sqrt(5))) or Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))). Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

How to calculate Inradius of Pentagon given Diagonal?

The Inradius of Pentagon given Diagonal formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using diagonal of Pentagon is calculated using Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5))). To calculate Inradius of Pentagon given Diagonal, you need Diagonal of Pentagon (d). With our tool, you need to enter the respective value for Diagonal of Pentagon 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 Inradius of Pentagon?

In this formula, Inradius of Pentagon uses Diagonal of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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