Height of Pentagon given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
h = P*sqrt(5+(2*sqrt(5)))/10
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.
Perimeter of Pentagon - (Measured in Meter) - The Perimeter of Pentagon is the total distance around the edge of the Pentagon.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Pentagon: 50 Meter --> 50 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = P*sqrt(5+(2*sqrt(5)))/10 --> 50*sqrt(5+(2*sqrt(5)))/10
Evaluating ... ...
h = 15.3884176858763
STEP 3: Convert Result to Output's Unit
15.3884176858763 Meter --> No Conversion Required
FINAL ANSWER
15.3884176858763 15.38842 Meter <-- Height of Pentagon
(Calculation completed in 00.004 seconds)

Credits

Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
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16 Height of Pentagon Calculators

Height of Pentagon given Area using Interior Angle
Go Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
Height of Pentagon given Area using Central Angle
Go Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
Height of Pentagon given Edge Length using Interior Angle
Go Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
Height of Pentagon given Area
Go Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
Height of Pentagon given Circumradius
Go Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon
Height of Pentagon given Edge Length using Central Angle
Go Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon given Diagonal
Go Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Width
Go Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Inradius using Interior Angle
Go Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
Height of Pentagon
Go Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
Height of Pentagon given Circumradius using Interior Angle
Go Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
Height of Pentagon given Perimeter
Go Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
Height of Pentagon given Circumradius using Central Angle
Go Height of Pentagon = Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon given Inradius using Central angle
Go Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5)))
Height of Pentagon given Circumradius and Inradius
Go Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon
Height of Pentagon given Inradius
Go Height of Pentagon = sqrt(5)*Inradius of Pentagon

Height of Pentagon given Perimeter Formula

Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
h = P*sqrt(5+(2*sqrt(5)))/10

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 Perimeter?

Height of Pentagon given Perimeter calculator uses Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10 to calculate the Height of Pentagon, The Height of Pentagon given Perimeter formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using the perimeter. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Perimeter using this online calculator? To use this online calculator for Height of Pentagon given Perimeter, enter Perimeter of Pentagon (P) and hit the calculate button. Here is how the Height of Pentagon given Perimeter calculation can be explained with given input values -> 15.38842 = 50*sqrt(5+(2*sqrt(5)))/10.

FAQ

What is Height of Pentagon given Perimeter?
The Height of Pentagon given Perimeter formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using the perimeter and is represented as h = P*sqrt(5+(2*sqrt(5)))/10 or Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10. The Perimeter of Pentagon is the total distance around the edge of the Pentagon.
How to calculate Height of Pentagon given Perimeter?
The Height of Pentagon given Perimeter formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using the perimeter is calculated using Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10. To calculate Height of Pentagon given Perimeter, you need Perimeter of Pentagon (P). With our tool, you need to enter the respective value for Perimeter 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 Perimeter of Pentagon. We can use 15 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)))
  • Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
  • Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon
  • Height of Pentagon = sqrt(5)*Inradius of Pentagon
  • Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
  • Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
  • Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
  • Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
  • Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
  • Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
  • Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
  • Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
  • Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
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