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Area of Pentagon given Circumradius 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 = \frac{5 \cdot {(r c \cdot \sin (\frac{π}{5}))}^{2}}{\tan (\frac{π}{5})}

A - Area of Pentagon?r_c - Circumradius of Pentagon?π - Archimedes' constant?

Area of Pentagon given Circumradius using Central Angle Example

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

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

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

192.5889 = \frac{5 \cdot {(9 \cdot \sin (\frac{3.1416}{5}))}^{2}}{\tan (\frac{3.1416}{5})}

192.5889m² = \frac{5 \cdot {(9m \cdot \sin (\frac{3.1416}{5}))}^{2}}{\tan (\frac{3.1416}{5})}

192.5889 = \frac{5 \cdot {(9 \cdot \sin (\frac{3.1416}{5}))}^{2}}{\tan (\frac{3.1416}{5})}

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Area of Pentagon given Circumradius using Central Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{5 \cdot {(9m \cdot \sin (\frac{π}{5}))}^{2}}{\tan (\frac{π}{5})}

Next Step Substitute values of Constants

∴

A = \frac{5 \cdot {(9m \cdot \sin (\frac{3.1416}{5}))}^{2}}{\tan (\frac{3.1416}{5})}

Next Step Prepare to Evaluate

∴

A = \frac{5 \cdot {(9 \cdot \sin (\frac{3.1416}{5}))}^{2}}{\tan (\frac{3.1416}{5})}

Next Step Evaluate

∴

A = 192.588944549769m²

LAST Step Rounding Answer

∴

A = 192.5889m²

Area of Pentagon given Circumradius 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

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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)

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 Circumradius using Central Angle?

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

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

FAQs on Area of Pentagon given Circumradius using Central Angle

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

The formula of Area of Pentagon given Circumradius using Central Angle is expressed as Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5). Here is an example- 192.5889 = (5*(9*sin(pi/5))^2)/tan(pi/5).

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

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

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

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

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

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