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Height of Pentagon given Area using Interior Angle Formula

GoHeight of Pentagon given Circumradius and Inradius Formula

GoHeight of Pentagon given Circumradius using Central Angle Formula

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Height of Pentagon is the distance between one side of Pentagon and its opposite vertex. Check FAQs

h = \sqrt{\frac{4 \cdot \tan (\frac{π}{5}) \cdot A}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot π)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

h - Height of Pentagon?A - Area of Pentagon?π - Archimedes' constant?

Height of Pentagon given Area using Interior Angle Example

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

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

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

15.2966 = \sqrt{\frac{4 \cdot \tan (\frac{3.1416}{5}) \cdot 170}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot 3.1416)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

15.2966m = \sqrt{\frac{4 \cdot \tan (\frac{3.1416}{5}) \cdot 170m²}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot 3.1416)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

15.2966 = \sqrt{\frac{4 \cdot \tan (\frac{3.1416}{5}) \cdot 170}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot 3.1416)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

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Height of Pentagon given Area using Interior Angle Solution

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

FIRST Step Consider the formula

h = \sqrt{\frac{4 \cdot \tan (\frac{π}{5}) \cdot A}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot π)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Variables

∴

h = \sqrt{\frac{4 \cdot \tan (\frac{π}{5}) \cdot 170m²}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot π)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Constants

∴

h = \sqrt{\frac{4 \cdot \tan (\frac{3.1416}{5}) \cdot 170m²}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot 3.1416)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Prepare to Evaluate

∴

h = \sqrt{\frac{4 \cdot \tan (\frac{3.1416}{5}) \cdot 170}{5}} \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot 3.1416)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Evaluate

∴

h = 15.2965658394327m

LAST Step Rounding Answer

∴

h = 15.2966m

Height of Pentagon given Area using Interior Angle Formula Elements

Variables

Constants

Functions

Height of Pentagon

Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagon

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

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)

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)

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 Height of Pentagon

Go Height of Pentagon given Circumradius and Inradius

h = r c + r i

Go Height of Pentagon given Circumradius using Central Angle

h = r c \cdot (1 + \cos (\frac{π}{5}))

Go Height of Pentagon given Inradius using Central angle

h = r i \cdot (1 + (\frac{1}{\cos (\frac{π}{5})}))

Go Height of Pentagon given Edge Length using Central Angle

h = \frac{l e}{2} \cdot \frac{1 + \cos (\frac{π}{5})}{\sin (\frac{π}{5})}

How to Evaluate Height of Pentagon given Area using Interior Angle?

Height of Pentagon given Area using Interior Angle evaluator uses Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi) to evaluate the Height of Pentagon, The Height of Pentagon given Area using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its area and interior angle. Height of Pentagon is denoted by h symbol.

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

FAQs on Height of Pentagon given Area using Interior Angle

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

The formula of Height of Pentagon given Area using Interior Angle is expressed as Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi). Here is an example- 15.29657 = sqrt((4*tan(pi/5)*170)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi).

How to calculate Height of Pentagon given Area using Interior Angle?

With Area of Pentagon (A) we can find Height of Pentagon given Area using Interior Angle using the formula - Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Pentagon?

Here are the different ways to Calculate Height of Pentagon-

Height of Pentagon=Circumradius of Pentagon+Inradius of Pentagon
Height of Pentagon=Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon=Inradius of Pentagon*(1+(1/cos(pi/5)))

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

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

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

Height of Pentagon given Area using Interior Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Pentagon given Area using Interior Angle can be measured.

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