## Area of Pentagon given Inradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
A = 5/2*ri^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
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 = 5/2*ri^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 --> 5/2*7^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
Evaluating ... ...
A = 178.002919361313
STEP 3: Convert Result to Output's Unit
178.002919361313 Square Meter --> No Conversion Required
178.002919361313 178.0029 Square Meter <-- Area of Pentagon
(Calculation completed in 00.020 seconds)
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## < 16 Area of Pentagon Calculators

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

## Area of Pentagon given Inradius using Interior Angle Formula

Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
A = 5/2*ri^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^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 Inradius using Interior Angle?

Area of Pentagon given Inradius using Interior Angle calculator uses Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 to calculate the Area of Pentagon, The Area of Pentagon given Inradius using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using inradius and interior angle. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Inradius using Interior Angle using this online calculator? To use this online calculator for Area of Pentagon given Inradius using Interior Angle, enter Inradius of Pentagon (ri) and hit the calculate button. Here is how the Area of Pentagon given Inradius using Interior Angle calculation can be explained with given input values -> 178.0029 = 5/2*7^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2.

### FAQ

What is Area of Pentagon given Inradius using Interior Angle?
The Area of Pentagon given Inradius using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using inradius and interior angle and is represented as A = 5/2*ri^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 or Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. 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 using Interior Angle?
The Area of Pentagon given Inradius using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using inradius and interior angle is calculated using Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. To calculate Area of Pentagon given Inradius using Interior Angle, you need Inradius of Pentagon (ri). 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 = 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*((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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