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Area of Decagon given Inradius Formula

GoArea of Decagon Formula

GoArea of Decagon given Diagonal across Five Sides Formula

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Area of Decagon is the amount of 2-dimensional space occupied by the Decagon. Check FAQs

A = \frac{5}{2} \cdot \frac{{(2 \cdot r i)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

A - Area of Decagon?r_i - Inradius of Decagon?

Area of Decagon given Inradius Example

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Here is how the Area of Decagon given Inradius equation looks like with Values.

Here is how the Area of Decagon given Inradius equation looks like with Units.

Here is how the Area of Decagon given Inradius equation looks like.

731.0693 = \frac{5}{2} \cdot \frac{{(2 \cdot 15)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

731.0693m² = \frac{5}{2} \cdot \frac{{(2 \cdot 15m)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

731.0693 = \frac{5}{2} \cdot \frac{{(2 \cdot 15)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Area of Decagon given Inradius Solution

Follow our step by step solution on how to calculate Area of Decagon given Inradius?

FIRST Step Consider the formula

A = \frac{5}{2} \cdot \frac{{(2 \cdot r i)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

A = \frac{5}{2} \cdot \frac{{(2 \cdot 15m)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

A = \frac{5}{2} \cdot \frac{{(2 \cdot 15)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

A = 731.069316524039m²

LAST Step Rounding Answer

∴

A = 731.0693m²

Area of Decagon given Inradius Formula Elements

Variables

Functions

Area of Decagon

Area of Decagon is the amount of 2-dimensional space occupied by the Decagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Decagon

Inradius of Decagon

Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Decagon

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 Decagon

Go Area of Decagon

A = \frac{5}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot S^{2}

Go Area of Decagon given Diagonal across Five Sides

A = \frac{5}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{d 5}{1 + \sqrt{5}})}^{2}

Go Area of Decagon given Diagonal across Four Sides

A = \frac{5}{2} \cdot \frac{{(d 4)}^{2}}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Go Area of Decagon given Diagonal across Three Sides

A = \frac{5}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}})}^{2}

How to Evaluate Area of Decagon given Inradius?

Area of Decagon given Inradius evaluator uses Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))) to evaluate the Area of Decagon, The Area of Decagon given Inradius formula is defined as the measure of the total 2d space that the surface of the object occupies of a Decagon, calculated using its inradius. Area of Decagon is denoted by A symbol.

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

FAQs on Area of Decagon given Inradius

What is the formula to find Area of Decagon given Inradius?

The formula of Area of Decagon given Inradius is expressed as Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))). Here is an example- 731.0693 = 5/2*(2*15)^2/sqrt(5+(2*sqrt(5))).

How to calculate Area of Decagon given Inradius?

With Inradius of Decagon (r_i) we can find Area of Decagon given Inradius using the formula - Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Decagon?

Here are the different ways to Calculate Area of Decagon-

Area of Decagon=5/2*sqrt(5+(2*sqrt(5)))*Side of Decagon^2
Area of Decagon=5/2*sqrt(5+(2*sqrt(5)))*(Diagonal across Five Sides of Decagon/(1+sqrt(5)))^2
Area of Decagon=5/2*(Diagonal across Four Sides of Decagon)^2/sqrt(5+(2*sqrt(5)))

Can the Area of Decagon given Inradius be negative?

No, the Area of Decagon given Inradius, measured in Area cannot be negative.

Which unit is used to measure Area of Decagon given Inradius?

Area of Decagon given Inradius 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 Decagon given Inradius can be measured.

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