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Area of Pentagon given Inradius using Interior Angle Formula

GoArea of Pentagon Formula

GoArea of Pentagon given Edge Length using Central Angle Formula

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The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon. Check FAQs

A = \frac{5}{2} \cdot {r i}^{2} \cdot \frac{\sin (\frac{3}{5} \cdot π)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}

A - Area of Pentagon?r_i - Inradius of Pentagon?π - Archimedes' constant?

Area of Pentagon given Inradius using Interior Angle Example

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Here is how the Area of Pentagon given Inradius using Interior Angle equation looks like with Values.

Here is how the Area of Pentagon given Inradius using Interior Angle equation looks like with Units.

Here is how the Area of Pentagon given Inradius using Interior Angle equation looks like.

178.0029 = \frac{5}{2} \cdot 7^{2} \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

178.0029m² = \frac{5}{2} \cdot {7m}^{2} \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

178.0029 = \frac{5}{2} \cdot 7^{2} \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

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Area of Pentagon given Inradius using Interior Angle Solution

Follow our step by step solution on how to calculate Area of Pentagon given Inradius using Interior Angle?

FIRST Step Consider the formula

A = \frac{5}{2} \cdot {r i}^{2} \cdot \frac{\sin (\frac{3}{5} \cdot π)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}

Next Step Substitute values of Variables

∴

A = \frac{5}{2} \cdot {7m}^{2} \cdot \frac{\sin (\frac{3}{5} \cdot π)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}

Next Step Substitute values of Constants

∴

A = \frac{5}{2} \cdot {7m}^{2} \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

Next Step Prepare to Evaluate

∴

A = \frac{5}{2} \cdot 7^{2} \cdot \frac{\sin (\frac{3}{5} \cdot 3.1416)}{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}

Next Step Evaluate

∴

A = 178.002919361313m²

LAST Step Rounding Answer

∴

A = 178.0029m²

Area of Pentagon given Inradius using Interior Angle Formula Elements

Variables

Constants

Functions

Area of Pentagon

The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Pentagon

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Area of Pentagon

Go Area of Pentagon

A = \frac{{l e}^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Go Area of Pentagon given Edge Length using Central Angle

A = \frac{5 \cdot {l e}^{2}}{4 \cdot \tan (\frac{π}{5})}

Go Area of Pentagon given Circumradius using Interior Angle

A = \frac{5}{2} \cdot {r c}^{2} \cdot \sin (\frac{3}{5} \cdot π)

Go Area of Pentagon given Edge Length and Inradius

A = \frac{5}{2} \cdot l e \cdot r i

How to Evaluate Area of Pentagon given Inradius using Interior Angle?

Area of Pentagon given Inradius using Interior Angle evaluator uses Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 to evaluate 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 evaluate Area of Pentagon given Inradius using Interior Angle using this online evaluator? To use this online evaluator for Area of Pentagon given Inradius using Interior Angle, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Area of Pentagon given Inradius using Interior Angle

What is the formula to find Area of Pentagon given Inradius using Interior Angle?

The formula of Area of Pentagon given Inradius using Interior Angle is expressed as Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. Here is an example- 178.0029 = 5/2*7^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2.

How to calculate Area of Pentagon given Inradius using Interior Angle?

With Inradius of Pentagon (r_i) we can find Area of Pentagon given Inradius using Interior Angle using the formula - Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Area of Pentagon?

Here are the different ways to Calculate Area of Pentagon-

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)

Can the Area of Pentagon given Inradius using Interior Angle be negative?

No, the Area of Pentagon given Inradius using Interior Angle, measured in Area cannot be negative.

Which unit is used to measure Area of Pentagon given Inradius using Interior Angle?

Area of Pentagon given Inradius using Interior Angle is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Pentagon given Inradius using Interior Angle can be measured.

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