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Area of Pentagon given Diagonal 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 = d^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

A - Area of Pentagon?d - Diagonal of Pentagon?

Area of Pentagon given Diagonal Example

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

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

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

168.234 = 16^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

168.234m² = {16m}^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

168.234 = 16^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

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Area of Pentagon given Diagonal Solution

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

FIRST Step Consider the formula

A = d^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

Next Step Substitute values of Variables

∴

A = {16m}^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

Next Step Prepare to Evaluate

∴

A = 16^{2} \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{{(1 + \sqrt{5})}^{2}}

Next Step Evaluate

∴

A = 168.233955878123m²

LAST Step Rounding Answer

∴

A = 168.234m²

Area of Pentagon given Diagonal 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

Diagonal of Pentagon

Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal 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 Diagonal?

Area of Pentagon given Diagonal evaluator uses Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2 to evaluate the Area of Pentagon, The Area of Pentagon given Diagonal formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using diagonal. Area of Pentagon is denoted by A symbol.

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

FAQs on Area of Pentagon given Diagonal

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

The formula of Area of Pentagon given Diagonal is expressed as Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2. Here is an example- 168.234 = 16^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2.

How to calculate Area of Pentagon given Diagonal?

With Diagonal of Pentagon (d) we can find Area of Pentagon given Diagonal using the formula - Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2. 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 Diagonal be negative?

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

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

Area of Pentagon given Diagonal 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 Diagonal can be measured.

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