Area of Pentagon given Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
A = d^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
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
Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.
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
A = d^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2 --> 16^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
Evaluating ... ...
A = 168.233955878123
STEP 3: Convert Result to Output's Unit
168.233955878123 Square Meter --> No Conversion Required
FINAL ANSWER
168.233955878123 168.234 Square Meter <-- Area of Pentagon
(Calculation completed in 00.004 seconds)

Credits

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Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
Divanshi Jain has created this Calculator and 300+ more calculators!
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Verified by Nayana Phulphagar
Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
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16 Area of Pentagon Calculators

Area of Pentagon given Height using Interior Angle
​ Go Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))
Area of Pentagon given Height using Central Angle
​ Go Area of Pentagon = (5*((2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5)))^2)/(4*tan(pi/5))
Area of Pentagon given Edge Length using Interior Angle
​ Go Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))
Area of Pentagon given Inradius using Interior Angle
​ Go Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
Area of Pentagon given Circumradius using Central Angle
​ Go Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5)
Area of Pentagon given Circumradius
​ Go Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))
Area of Pentagon given Diagonal
​ Go Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
Area of Pentagon given Height
​ Go Area of Pentagon = Height of Pentagon^2*sqrt(25+(10*sqrt(5)))/(5+(2*sqrt(5)))
Area of Pentagon given Width
​ Go Area of Pentagon = Width of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
Area of Pentagon given Perimeter
​ Go Area of Pentagon = Perimeter of Pentagon^2*sqrt(25+(10*sqrt(5)))/100
Area of Pentagon
​ Go Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
Area of Pentagon given Inradius
​ Go Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5)))
Area of Pentagon given Edge Length using Central Angle
​ Go Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))
Area of Pentagon given Circumradius using Interior Angle
​ Go Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)
Area of Pentagon given Inradius using Central Angle
​ Go Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5)
Area of Pentagon given Edge Length and Inradius
​ Go Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon

Area of Pentagon given Diagonal Formula

Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
A = d^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2

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 Area of Pentagon given Diagonal?

Area of Pentagon given Diagonal calculator uses Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2 to calculate the Area of Pentagon, The Area of Pentagon given Diagonal formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using diagonal. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Diagonal using this online calculator? To use this online calculator for Area of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button. Here is how the Area of Pentagon given Diagonal calculation can be explained with given input values -> 168.234 = 16^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2.

FAQ

What is Area of Pentagon given Diagonal?
The Area of Pentagon given Diagonal formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using diagonal and is represented as A = d^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2 or Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2. Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.
How to calculate Area of Pentagon given Diagonal?
The Area of Pentagon given Diagonal formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using diagonal is calculated using Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2. To calculate Area 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 Area of Pentagon?
In this formula, Area of Pentagon uses Diagonal of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -
  • Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
  • Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))
  • Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)
  • Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon
  • Area of Pentagon = Perimeter of Pentagon^2*sqrt(25+(10*sqrt(5)))/100
  • Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))
  • Area of Pentagon = Height of Pentagon^2*sqrt(25+(10*sqrt(5)))/(5+(2*sqrt(5)))
  • Area of Pentagon = Width of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
  • Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5)))
  • Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5)
  • Area of Pentagon = (5*((2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5)))^2)/(4*tan(pi/5))
  • Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5)
  • Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))
  • Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
  • Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))
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