Area of Pentagon given Edge Length and Inradius Calculator

✖The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon [l_e]			+10% -10%
✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon [r_i]			+10% -10%

✖The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.ⓘ Area of Pentagon given Edge Length and Inradius [A]

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Formula

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Area of Pentagon given Edge Length and Inradius

Formula

`"A" = 5/2*"l"_{"e"}*"r"_{"i"}`

Example

`"175m²"= 5/2*"10m"*"7m"`

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Area of Pentagon given Edge Length and Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon
A = 5/2*l_e*r_i
This formula uses 3 Variables

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.
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

Edge Length of Pentagon: 10 Meter --> 10 Meter No Conversion Required
Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 5/2*l_e*r_i --> 5/2*10*7

Evaluating ... ...

A = 175

STEP 3: Convert Result to Output's Unit

175 Square Meter --> No Conversion Required

FINAL ANSWER

175 Square Meter <-- Area of Pentagon

(Calculation completed in 00.008 seconds)

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Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Shashwati Tidke

Vishwakarma Institute of Technology (VIT), Pune

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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 given Edge Length and Inradius Formula

Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon
A = 5/2*l_e*r_i

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 is 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 Edge Length and Inradius?

Area of Pentagon given Edge Length and Inradius calculator uses Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon to calculate the Area of Pentagon, Area of Pentagon given Edge Length and Inradius is defined as the 2-dimensional space occupied by a Pentagon, calculated using edge length and inradius. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Edge Length and Inradius using this online calculator? To use this online calculator for Area of Pentagon given Edge Length and Inradius, enter Edge Length of Pentagon (l_e) & Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Area of Pentagon given Edge Length and Inradius calculation can be explained with given input values -> 175 = 5/2*10*7.

FAQ

What is Area of Pentagon given Edge Length and Inradius?

Area of Pentagon given Edge Length and Inradius is defined as the 2-dimensional space occupied by a Pentagon, calculated using edge length and inradius and is represented as A = 5/2*l_e*r_i or Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon. The Edge Length of Pentagon is the length of one of the five sides of the Pentagon & The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

How to calculate Area of Pentagon given Edge Length and Inradius?

Area of Pentagon given Edge Length and Inradius is defined as the 2-dimensional space occupied by a Pentagon, calculated using edge length and inradius is calculated using Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon. To calculate Area of Pentagon given Edge Length and Inradius, you need Edge Length of Pentagon (l_e) & Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for Edge Length 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 Area of Pentagon?

In this formula, Area of Pentagon uses Edge Length of Pentagon & Inradius of Pentagon. We can use 18 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 = 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 = 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*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))

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