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Area of Pentagon given Circumradius 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 = {r c}^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

A - Area of Pentagon?r_c - Circumradius of Pentagon?

Area of Pentagon given Circumradius Example

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

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

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

192.5889 = 9^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

192.5889m² = {9m}^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

192.5889 = 9^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

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Area of Pentagon given Circumradius Solution

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

FIRST Step Consider the formula

A = {r c}^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

Next Step Substitute values of Variables

∴

A = {9m}^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

Next Step Prepare to Evaluate

∴

A = 9^{2} \cdot 25 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50 + (10 \cdot \sqrt{5})}

Next Step Evaluate

∴

A = 192.588944549769m²

LAST Step Rounding Answer

∴

A = 192.5889m²

Area of Pentagon given Circumradius Formula Elements

Variables

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

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 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?

Area of Pentagon given Circumradius evaluator uses Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))) to evaluate the Area of Pentagon, Area of Pentagon given Circumradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using circumradius. Area of Pentagon is denoted by A symbol.

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

FAQs on Area of Pentagon given Circumradius

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

The formula of Area of Pentagon given Circumradius is expressed as Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))). Here is an example- 192.5889 = 9^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))).

How to calculate Area of Pentagon given Circumradius?

With Circumradius of Pentagon (r_c) we can find Area of Pentagon given Circumradius using the formula - Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))). This formula also uses Square Root (sqrt) 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 be negative?

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

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

Area of Pentagon given Circumradius 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 can be measured.

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