Height of Pentagon given Area Calculator

Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
h = sqrt(5+(2*sqrt(5)))/2*sqrt(4*A/sqrt(25+(10*sqrt(5))))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

STEP 1: Convert Input(s) to Base Unit

Area of Pentagon: 170 Square Meter --> 170 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(5+(2*sqrt(5)))/2*sqrt(4*A/sqrt(25+(10*sqrt(5)))) --> sqrt(5+(2*sqrt(5)))/2*sqrt(4*170/sqrt(25+(10*sqrt(5))))

Evaluating ... ...

h = 15.2965658394327

STEP 3: Convert Result to Output's Unit

15.2965658394327 Meter --> No Conversion Required

FINAL ANSWER

15.2965658394327 ≈ 15.29657 Meter <-- Height of Pentagon

(Calculation completed in 00.004 seconds)

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Credits

Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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< 16 Height of Pentagon Calculators

Height of Pentagon given Area using Interior Angle

Go 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)

Height of Pentagon given Area using Central Angle

Go Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))

Height of Pentagon given Edge Length using Interior Angle

Go Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)

Height of Pentagon given Area

Go Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))

Height of Pentagon given Circumradius

Go Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon

Height of Pentagon given Edge Length using Central Angle

Go Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)

Height of Pentagon given Diagonal

Go Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))

Height of Pentagon given Width

Go Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))

Height of Pentagon given Inradius using Interior Angle

Go Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))

Height of Pentagon

Go Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))

Height of Pentagon given Circumradius using Interior Angle

Go Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))

Height of Pentagon given Perimeter

Go Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10

Height of Pentagon given Circumradius using Central Angle

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

Height of Pentagon given Inradius using Central angle

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

Height of Pentagon given Circumradius and Inradius

Go Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon

Height of Pentagon given Inradius

Go Height of Pentagon = sqrt(5)*Inradius of Pentagon

Height of Pentagon given Area Formula

Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
h = sqrt(5+(2*sqrt(5)))/2*sqrt(4*A/sqrt(25+(10*sqrt(5))))

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

How to Calculate Height of Pentagon given Area?

Height of Pentagon given Area calculator uses Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))) to calculate the Height of Pentagon, The Height of Pentagon given Area formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using area. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Area using this online calculator? To use this online calculator for Height of Pentagon given Area, enter Area of Pentagon (A) and hit the calculate button. Here is how the Height of Pentagon given Area calculation can be explained with given input values -> 15.29657 = sqrt(5+(2*sqrt(5)))/2*sqrt(4*170/sqrt(25+(10*sqrt(5)))).

FAQ

What is Height of Pentagon given Area?

The Height of Pentagon given Area formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using area and is represented as h = sqrt(5+(2*sqrt(5)))/2*sqrt(4*A/sqrt(25+(10*sqrt(5)))) or Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))). The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.

How to calculate Height of Pentagon given Area?

The Height of Pentagon given Area formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using area is calculated using Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5)))). To calculate Height of Pentagon given Area, you need Area of Pentagon (A). With our tool, you need to enter the respective value for Area of Pentagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of Pentagon?

In this formula, Height of Pentagon uses Area of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -

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)))
Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon
Height of Pentagon = sqrt(5)*Inradius of Pentagon
Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
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)
Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)

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