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Area of Pentagon Formula

GoArea of Pentagon given Edge Length and Inradius 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{{l e}^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

A - Area of Pentagon?l_e - Edge Length of Pentagon?

Area of Pentagon Example

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

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

Here is how the Area of Pentagon equation looks like.

172.0477 = \frac{10^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

172.0477m² = \frac{{10m}^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

172.0477 = \frac{10^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

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Area of Pentagon Solution

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

FIRST Step Consider the formula

A = \frac{{l e}^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Next Step Substitute values of Variables

∴

A = \frac{{10m}^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Next Step Prepare to Evaluate

∴

A = \frac{10^{2}}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Next Step Evaluate

∴

A = 172.047740058897m²

LAST Step Rounding Answer

∴

A = 172.0477m²

Area of Pentagon 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

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

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 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})}

Go Area of Pentagon given Edge Length using Interior Angle

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)}

How to Evaluate Area of Pentagon?

Area of Pentagon evaluator uses Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5))) to evaluate the Area of Pentagon, Area of Pentagon is defined as the amount of 2-dimensional space occupied by a Pentagon. Area of Pentagon is denoted by A symbol.

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

FAQs on Area of Pentagon

What is the formula to find Area of Pentagon?

The formula of Area of Pentagon is expressed as Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5))). Here is an example- 172.0477 = 10^2/4*sqrt(25+(10*sqrt(5))).

How to calculate Area of Pentagon?

With Edge Length of Pentagon (l_e) we can find Area of Pentagon using the formula - Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(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=5/2*Edge Length of Pentagon*Inradius of Pentagon
Area of Pentagon=(5*Edge Length of Pentagon^2)/(4*tan(pi/5))
Area of Pentagon=(5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))

Can the Area of Pentagon be negative?

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

Which unit is used to measure Area of Pentagon?

Area of Pentagon 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 can be measured.

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