Inradius of Pentagon given Area Calculator

✖The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.ⓘ Area of Pentagon [A]

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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 Area [r_i]

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Inradius of Pentagon given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
r_i = sqrt(25+(10*sqrt(5)))/10*sqrt(4*A/sqrt(25+(10*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.
Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

STEP 1: Convert Input(s) to Base Unit

Area of Pentagon: 170 Square Meter --> 170 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt(25+(10*sqrt(5)))/10*sqrt(4*A/sqrt(25+(10*sqrt(5)))) --> sqrt(25+(10*sqrt(5)))/10*sqrt(4*170/sqrt(25+(10*sqrt(5))))

Evaluating ... ...

r_i = 6.84083220785453

STEP 3: Convert Result to Output's Unit

6.84083220785453 Meter --> No Conversion Required

FINAL ANSWER

6.84083220785453 ≈ 6.840832 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 Area Formula

LaTeX Go

Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
r_i = sqrt(25+(10*sqrt(5)))/10*sqrt(4*A/sqrt(25+(10*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 Area?

Inradius of Pentagon given Area calculator uses Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))) to calculate the Inradius of Pentagon, The Inradius of Pentagon given Area formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using area of Pentagon. Inradius of Pentagon is denoted by r_i symbol.

How to calculate Inradius of Pentagon given Area using this online calculator? To use this online calculator for Inradius of Pentagon given Area, enter Area of Pentagon (A) and hit the calculate button. Here is how the Inradius of Pentagon given Area calculation can be explained with given input values -> 6.840832 = sqrt(25+(10*sqrt(5)))/10*sqrt(4*170/sqrt(25+(10*sqrt(5)))).

FAQ

What is Inradius of Pentagon given Area?

The Inradius of Pentagon given Area formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using area of Pentagon and is represented as r_i = sqrt(25+(10*sqrt(5)))/10*sqrt(4*A/sqrt(25+(10*sqrt(5)))) or Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))). The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

How to calculate Inradius of Pentagon given Area?

The Inradius of Pentagon given Area formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using area of Pentagon is calculated using Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))). To calculate Inradius of Pentagon given Area, you need Area of Pentagon (A). With our tool, you need to enter the respective value for Area 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 Area 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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