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Area of Pentagon given Edge Length using Interior Angle Formula

GoArea of Pentagon Formula

GoArea of Pentagon given Edge Length and Inradius 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 {l e}^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot π)}

A - Area of Pentagon?l_e - Edge Length of Pentagon?π - Archimedes' constant?

Area of Pentagon given Edge Length using Interior Angle Example

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Here is how the Area of Pentagon given Edge Length using Interior Angle equation looks like with Values.

Here is how the Area of Pentagon given Edge Length using Interior Angle equation looks like with Units.

Here is how the Area of Pentagon given Edge Length using Interior Angle equation looks like.

172.0477 = \frac{5 \cdot 10^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot 3.1416)}

172.0477m² = \frac{5 \cdot {10m}^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot 3.1416)}

172.0477 = \frac{5 \cdot 10^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot 3.1416)}

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Area of Pentagon given Edge Length using Interior Angle Solution

Follow our step by step solution on how to calculate Area of Pentagon given Edge Length using Interior Angle?

FIRST Step Consider the formula

A = \frac{5 \cdot {l e}^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Variables

∴

A = \frac{5 \cdot {10m}^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Constants

∴

A = \frac{5 \cdot {10m}^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot 3.1416)}

Next Step Prepare to Evaluate

∴

A = \frac{5 \cdot 10^{2} \cdot {(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2}}{2 \cdot \sin (\frac{3}{5} \cdot 3.1416)}

Next Step Evaluate

∴

A = 172.047740058897m²

LAST Step Rounding Answer

∴

A = 172.0477m²

Area of Pentagon given Edge Length using Interior 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

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(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 and Inradius

A = \frac{5}{2} \cdot l e \cdot r i

Go Area of Pentagon given Edge Length using Central Angle

A = \frac{5 \cdot {l e}^{2}}{4 \cdot \tan (\frac{π}{5})}

How to Evaluate Area of Pentagon given Edge Length using Interior Angle?

Area of Pentagon given Edge Length using Interior Angle evaluator uses Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi)) to evaluate the Area of Pentagon, The Area of Pentagon given Edge Length using Interior Angle is defined as the space occupied by the Pentagon in space., calculated using edge length and interior angle. Area of Pentagon is denoted by A symbol.

How to evaluate Area of Pentagon given Edge Length using Interior Angle using this online evaluator? To use this online evaluator for Area of Pentagon given Edge Length using Interior Angle, enter Edge Length of Pentagon (l_e) and hit the calculate button.

FAQs on Area of Pentagon given Edge Length using Interior Angle

What is the formula to find Area of Pentagon given Edge Length using Interior Angle?

The formula of Area of Pentagon given Edge Length using Interior Angle is expressed as Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi)). Here is an example- 172.0477 = (5*10^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi)).

How to calculate Area of Pentagon given Edge Length using Interior Angle?

With Edge Length of Pentagon (l_e) we can find Area of Pentagon given Edge Length using Interior Angle using the formula - Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi)). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) 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=5/2*Edge Length of Pentagon*Inradius of Pentagon
Area of Pentagon=(5*Edge Length of Pentagon^2)/(4*tan(pi/5))

Can the Area of Pentagon given Edge Length using Interior Angle be negative?

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

Which unit is used to measure Area of Pentagon given Edge Length using Interior Angle?

Area of Pentagon given Edge Length using Interior 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 Edge Length using Interior Angle can be measured.

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