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Area of Pentagon given Inradius using Central 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 = 5 \cdot {r i}^{2} \cdot \tan (\frac{π}{5})

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

Area of Pentagon given Inradius using Central Angle Example

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

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

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

178.0029 = 5 \cdot 7^{2} \cdot \tan (\frac{3.1416}{5})

178.0029m² = 5 \cdot {7m}^{2} \cdot \tan (\frac{3.1416}{5})

178.0029 = 5 \cdot 7^{2} \cdot \tan (\frac{3.1416}{5})

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Area of Pentagon given Inradius using Central Angle Solution

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

FIRST Step Consider the formula

A = 5 \cdot {r i}^{2} \cdot \tan (\frac{π}{5})

Next Step Substitute values of Variables

∴

A = 5 \cdot {7m}^{2} \cdot \tan (\frac{π}{5})

Next Step Substitute values of Constants

∴

A = 5 \cdot {7m}^{2} \cdot \tan (\frac{3.1416}{5})

Next Step Prepare to Evaluate

∴

A = 5 \cdot 7^{2} \cdot \tan (\frac{3.1416}{5})

Next Step Evaluate

∴

A = 178.002919361313m²

LAST Step Rounding Answer

∴

A = 178.0029m²

Area of Pentagon given Inradius using Central 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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(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 Central Angle?

Area of Pentagon given Inradius using Central Angle evaluator uses Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5) to evaluate the Area of Pentagon, The Area of Pentagon given Inradius using Central Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using inradius and central angle. Area of Pentagon is denoted by A symbol.

How to evaluate Area of Pentagon given Inradius using Central Angle using this online evaluator? To use this online evaluator for Area of Pentagon given Inradius using Central Angle, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Area of Pentagon given Inradius using Central Angle

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

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

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

With Inradius of Pentagon (r_i) we can find Area of Pentagon given Inradius using Central Angle using the formula - Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5). This formula also uses Archimedes' constant and Tangent (tan) 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 Central Angle be negative?

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

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

Area of Pentagon given Inradius using Central 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 Central Angle can be measured.

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