Area of Pentagon given Inradius Calculator

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.
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

Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 25*r_i^2/sqrt(25+(10*sqrt(5))) --> 25*7^2/sqrt(25+(10*sqrt(5)))

Evaluating ... ...

A = 178.002919361313

STEP 3: Convert Result to Output's Unit

178.002919361313 Square Meter --> No Conversion Required

FINAL ANSWER

178.002919361313 ≈ 178.0029 Square Meter <-- Area of Pentagon

(Calculation completed in 00.020 seconds)

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Credits

Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

Divanshi Jain has created this Calculator and 300+ more calculators!

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 Inradius Formula

Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5)))
A = 25*r_i^2/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 given Inradius?

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

How to calculate Area of Pentagon given Inradius using this online calculator? To use this online calculator for Area of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Area of Pentagon given Inradius calculation can be explained with given input values -> 178.0029 = 25*7^2/sqrt(25+(10*sqrt(5))).

FAQ

What is Area of Pentagon given Inradius?

The Area of Pentagon given Inradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using inradius and is represented as A = 25*r_i^2/sqrt(25+(10*sqrt(5))) or Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5))). 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 Inradius?

The Area of Pentagon given Inradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using inradius is calculated using Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5))). To calculate Area of Pentagon given Inradius, you need Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for 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 Inradius 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 = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
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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