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

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Height of Pentagon given Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
h = d*sqrt(5+(2*sqrt(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

Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
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

h = d*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)) --> 16*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))

Evaluating ... ...

h = 15.2169042607225

STEP 3: Convert Result to Output's Unit

15.2169042607225 Meter --> No Conversion Required

FINAL ANSWER

15.2169042607225 ≈ 15.2169 Meter <-- Height of Pentagon

(Calculation completed in 00.020 seconds)

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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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 Diagonal Formula

LaTeX Go

Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
h = d*sqrt(5+(2*sqrt(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 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 Diagonal?

Height of Pentagon given Diagonal calculator uses Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)) to calculate the Height of Pentagon, The Height of Pentagon given Diagonal formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using a diagonal. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Diagonal using this online calculator? To use this online calculator for Height of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button. Here is how the Height of Pentagon given Diagonal calculation can be explained with given input values -> 15.2169 = 16*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)).

FAQ

What is Height of Pentagon given Diagonal?

The Height of Pentagon given Diagonal formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using a diagonal and is represented as h = d*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)) or Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)). Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

How to calculate Height of Pentagon given Diagonal?

The Height of Pentagon given Diagonal formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using a diagonal is calculated using Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)). To calculate Height 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 Height of Pentagon?

In this formula, Height of Pentagon uses Diagonal 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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