Height of Pentagon given Circumradius and Inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon
h = rc+ri
This formula uses 3 Variables
Variables Used
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
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
Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required
Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = rc+ri --> 9+7
Evaluating ... ...
h = 16
STEP 3: Convert Result to Output's Unit
16 Meter --> No Conversion Required
FINAL ANSWER
16 Meter <-- Height of Pentagon
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has created this Calculator and 2500+ more calculators!
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St Joseph's College (SJC), Bengaluru
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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

4 Height of Pentagon Calculators

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 Edge Length using Central Angle
Go Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon
Go Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
Height of Pentagon given Circumradius and Inradius
Go Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon

Height of Pentagon given Circumradius and Inradius Formula

Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon
h = rc+ri

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 Circumradius and Inradius?

Height of Pentagon given Circumradius and Inradius calculator uses Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon to calculate the Height of Pentagon, Height of Pentagon given Circumradius and Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and inradius. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Circumradius and Inradius using this online calculator? To use this online calculator for Height of Pentagon given Circumradius and Inradius, enter Circumradius of Pentagon (rc) & Inradius of Pentagon (ri) and hit the calculate button. Here is how the Height of Pentagon given Circumradius and Inradius calculation can be explained with given input values -> 16 = 9+7 .

FAQ

What is Height of Pentagon given Circumradius and Inradius?
Height of Pentagon given Circumradius and Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and inradius and is represented as h = rc+ri or Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon. The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices 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 Circumradius and Inradius?
Height of Pentagon given Circumradius and Inradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and inradius is calculated using Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon. To calculate Height of Pentagon given Circumradius and Inradius, you need Circumradius of Pentagon (rc) & Inradius of Pentagon (ri). With our tool, you need to enter the respective value for Circumradius of Pentagon & 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 Circumradius of Pentagon & Inradius of Pentagon. We can use 18 other way(s) to calculate the same, which is/are as follows -
  • 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 = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
  • 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)
  • Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
  • Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
  • 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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