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Area of Heptagon given Inradius Formula

GoArea of Heptagon given Long Diagonal Formula

GoArea of Heptagon given Short Diagonal Formula

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The Area of Heptagon is the amount of two-dimensional space taken up by the Heptagon. Check FAQs

A = \frac{7}{4} \cdot \frac{{(r i \cdot 2 \cdot \tan (\frac{π}{7}))}^{2}}{\tan (\frac{π}{7})}

A - Area of Heptagon?r_i - Inradius of Heptagon?π - Archimedes' constant?

Area of Heptagon given Inradius Example

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

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

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

407.8937 = \frac{7}{4} \cdot \frac{{(11 \cdot 2 \cdot \tan (\frac{3.1416}{7}))}^{2}}{\tan (\frac{3.1416}{7})}

407.8937m² = \frac{7}{4} \cdot \frac{{(11m \cdot 2 \cdot \tan (\frac{3.1416}{7}))}^{2}}{\tan (\frac{3.1416}{7})}

407.8937 = \frac{7}{4} \cdot \frac{{(11 \cdot 2 \cdot \tan (\frac{3.1416}{7}))}^{2}}{\tan (\frac{3.1416}{7})}

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Area of Heptagon given Inradius Solution

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

FIRST Step Consider the formula

A = \frac{7}{4} \cdot \frac{{(r i \cdot 2 \cdot \tan (\frac{π}{7}))}^{2}}{\tan (\frac{π}{7})}

Next Step Substitute values of Variables

∴

A = \frac{7}{4} \cdot \frac{{(11m \cdot 2 \cdot \tan (\frac{π}{7}))}^{2}}{\tan (\frac{π}{7})}

Next Step Substitute values of Constants

∴

A = \frac{7}{4} \cdot \frac{{(11m \cdot 2 \cdot \tan (\frac{3.1416}{7}))}^{2}}{\tan (\frac{3.1416}{7})}

Next Step Prepare to Evaluate

∴

A = \frac{7}{4} \cdot \frac{{(11 \cdot 2 \cdot \tan (\frac{3.1416}{7}))}^{2}}{\tan (\frac{3.1416}{7})}

Next Step Evaluate

∴

A = 407.893702129977m²

LAST Step Rounding Answer

∴

A = 407.8937m²

Area of Heptagon given Inradius Formula Elements

Variables

Constants

Functions

Area of Heptagon

The Area of Heptagon is the amount of two-dimensional space taken up by the Heptagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Heptagon

Inradius of Heptagon

Inradius of Heptagon is defined as the radius of the circle which is inscribed inside the Heptagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Heptagon

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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Area of Heptagon

Go Area of Heptagon given Long Diagonal

A = \frac{7}{4} \cdot \frac{{(d Long \cdot 2 \cdot \sin (\frac{(\frac{π}{2})}{7}))}^{2}}{\tan (\frac{π}{7})}

Go Area of Heptagon given Short Diagonal

A = \frac{7}{4} \cdot \frac{{(\frac{d Short}{2 \cdot \cos (\frac{π}{7})})}^{2}}{\tan (\frac{π}{7})}

Go Area of Heptagon given Height

A = \frac{7}{4} \cdot \frac{{(2 \cdot h \cdot \tan (\frac{(\frac{π}{2})}{7}))}^{2}}{\tan (\frac{π}{7})}

Go Area of Heptagon given Perimeter

A = \frac{7}{4} \cdot \frac{{(\frac{P}{7})}^{2}}{\tan (\frac{π}{7})}

Other formulas in Area of Heptagon category

Go Area of Triangle of Heptagon given Inradius

A Triangle = \frac{1}{2} \cdot S \cdot r i

How to Evaluate Area of Heptagon given Inradius?

Area of Heptagon given Inradius evaluator uses Area of Heptagon = 7/4*(Inradius of Heptagon*2*tan(pi/7))^2/tan(pi/7) to evaluate the Area of Heptagon, The Area of Heptagon given Inradius formula is defined as the amount of space occupied by the surface inside the Heptagon, calculated using inradius. Area of Heptagon is denoted by A symbol.

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

FAQs on Area of Heptagon given Inradius

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

The formula of Area of Heptagon given Inradius is expressed as Area of Heptagon = 7/4*(Inradius of Heptagon*2*tan(pi/7))^2/tan(pi/7). Here is an example- 407.8937 = 7/4*(11*2*tan(pi/7))^2/tan(pi/7).

How to calculate Area of Heptagon given Inradius?

With Inradius of Heptagon (r_i) we can find Area of Heptagon given Inradius using the formula - Area of Heptagon = 7/4*(Inradius of Heptagon*2*tan(pi/7))^2/tan(pi/7). This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Area of Heptagon?

Here are the different ways to Calculate Area of Heptagon-

Area of Heptagon=7/4*((Long Diagonal of Heptagon*2*sin(((pi/2))/7))^2)/tan(pi/7)
Area of Heptagon=7/4*((Short Diagonal of Heptagon/(2*cos(pi/7)))^2)/tan(pi/7)
Area of Heptagon=7/4*((2*Height of Heptagon*tan(((pi/2))/7))^2)/tan(pi/7)

Can the Area of Heptagon given Inradius be negative?

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

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

Area of Heptagon 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 Heptagon given Inradius can be measured.

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