Height of Pentagon given Inradius Calculator

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

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✖Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.ⓘ Height of Pentagon given Inradius [h]

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Height of Pentagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Pentagon = sqrt(5)*Inradius of Pentagon
h = sqrt(5)*r_i
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

Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(5)*r_i --> sqrt(5)*7

Evaluating ... ...

h = 15.6524758424985

STEP 3: Convert Result to Output's Unit

15.6524758424985 Meter --> No Conversion Required

FINAL ANSWER

15.6524758424985 ≈ 15.65248 Meter <-- Height of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< Height of Pentagon Calculators

Height of Pentagon given Edge Length using Central Angle

LaTeX Go Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)

Height of Pentagon given Circumradius using Central Angle

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

Height of Pentagon given Inradius using Central angle

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

Height of Pentagon given Circumradius and Inradius

LaTeX Go Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon

Height of Pentagon given Inradius Formula

LaTeX Go

Height of Pentagon = sqrt(5)*Inradius of Pentagon
h = sqrt(5)*r_i

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 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 Height of Pentagon given Inradius?

Height of Pentagon given Inradius calculator uses Height of Pentagon = sqrt(5)*Inradius of Pentagon to calculate the Height of Pentagon, Height of Pentagon given Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Inradius using this online calculator? To use this online calculator for Height of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Height of Pentagon given Inradius calculation can be explained with given input values -> 15.65248 = sqrt(5)*7.

FAQ

What is Height of Pentagon given Inradius?

Height of Pentagon given Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius and is represented as h = sqrt(5)*r_i or Height of Pentagon = sqrt(5)*Inradius of Pentagon. The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

How to calculate Height of Pentagon given Inradius?

Height of Pentagon given Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius is calculated using Height of Pentagon = sqrt(5)*Inradius of Pentagon. To calculate Height of Pentagon given Inradius, you need Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Height of Pentagon?

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

Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon
Height of Pentagon = Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5)))

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