Area of Pentagon Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
A = le^2/4*sqrt(25+(10*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
Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.
Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Pentagon: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = le^2/4*sqrt(25+(10*sqrt(5))) --> 10^2/4*sqrt(25+(10*sqrt(5)))
Evaluating ... ...
A = 172.047740058897
STEP 3: Convert Result to Output's Unit
172.047740058897 Square Meter --> No Conversion Required
FINAL ANSWER
172.047740058897 172.0477 Square Meter <-- Area 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!
Verified by Mona Gladys
St Joseph's College (SJC), Bengaluru
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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

4 Area of Pentagon Calculators

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
Go Area of Pentagon = Edge Length of Pentagon^2/4*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 Edge Length and Inradius
Go Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon

Area of Pentagon Formula

Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
A = le^2/4*sqrt(25+(10*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 Area of Pentagon?

Area of Pentagon calculator uses Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5))) to calculate the Area of Pentagon, Area of Pentagon is defined as the amount of 2-dimensional space occupied by a Pentagon. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon using this online calculator? To use this online calculator for Area of Pentagon, enter Edge Length of Pentagon (le) and hit the calculate button. Here is how the Area of Pentagon calculation can be explained with given input values -> 172.0477 = 10^2/4*sqrt(25+(10*sqrt(5))).

FAQ

What is Area of Pentagon?
Area of Pentagon is defined as the amount of 2-dimensional space occupied by a Pentagon and is represented as A = le^2/4*sqrt(25+(10*sqrt(5))) or Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5))). The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
How to calculate Area of Pentagon?
Area of Pentagon is defined as the amount of 2-dimensional space occupied by a Pentagon is calculated using Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5))). To calculate Area of Pentagon, you need Edge Length of Pentagon (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Pentagon. We can use 18 other way(s) to calculate the same, which is/are as follows -
  • 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 = Diagonal 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))
  • Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon
  • Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))
  • Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))
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