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Circumradius of Pentagon given Area using Central Angle Formula

GoCircumradius of Pentagon given Edge Length using Central Angle Formula

GoCircumradius of Pentagon given Inradius Formula

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

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

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

Circumradius of Pentagon given Area using Central Angle Example

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

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

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

8.4557 = \sqrt{\frac{170 \cdot 2}{\sin (2 \cdot \frac{3.1416}{5}) \cdot 5}}

8.4557m = \sqrt{\frac{170m² \cdot 2}{\sin (2 \cdot \frac{3.1416}{5}) \cdot 5}}

8.4557 = \sqrt{\frac{170 \cdot 2}{\sin (2 \cdot \frac{3.1416}{5}) \cdot 5}}

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Circumradius of Pentagon given Area using Central Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \sqrt{\frac{170m² \cdot 2}{\sin (2 \cdot \frac{π}{5}) \cdot 5}}

Next Step Substitute values of Constants

∴

r c = \sqrt{\frac{170m² \cdot 2}{\sin (2 \cdot \frac{3.1416}{5}) \cdot 5}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{\frac{170 \cdot 2}{\sin (2 \cdot \frac{3.1416}{5}) \cdot 5}}

Next Step Evaluate

∴

r c = 8.45573363157817m

LAST Step Rounding Answer

∴

r c = 8.4557m

Circumradius of Pentagon given Area using Central Angle Formula Elements

Variables

Constants

Functions

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

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

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)

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.

Syntax: sqrt(Number)

Other Formulas to find Circumradius of Pentagon

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon given Inradius

r c = \frac{r i}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Inradius using Central Angle

r c = \frac{r i}{\cos (\frac{π}{5})}

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

Circumradius of Pentagon given Area using Central Angle evaluator uses Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5)) to evaluate the Circumradius of Pentagon, Circumradius of Pentagon given Area using Central Angle is defined as the length of line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and central angle. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQs on Circumradius of Pentagon given Area using Central Angle

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

The formula of Circumradius of Pentagon given Area using Central Angle is expressed as Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5)). Here is an example- 8.455734 = sqrt((170*2)/(sin(2*pi/5)*5)).

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

With Area of Pentagon (A) we can find Circumradius of Pentagon given Area using Central Angle using the formula - Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5)). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Pentagon?

Here are the different ways to Calculate Circumradius of Pentagon-

Circumradius of Pentagon=(Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon=(Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))
Circumradius of Pentagon=Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))

Can the Circumradius of Pentagon given Area using Central Angle be negative?

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

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

Circumradius of Pentagon given Area using Central Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Pentagon given Area using Central Angle can be measured.

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