## Height of Pentagon given Area using Central Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
h = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*A)/5))/(2*sin(pi/5))
This formula uses 1 Constants, 4 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
tan - Trigonometric tangent function, tan(Angle)
sqrt - Square root function, 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 = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*A)/5))/(2*sin(pi/5)) --> ((1+cos(pi/5))*sqrt((4*tan(pi/5)*170)/5))/(2*sin(pi/5))
Evaluating ... ...
h = 15.2965658394327
STEP 3: Convert Result to Output's Unit
15.2965658394327 Meter --> No Conversion Required
15.2965658394327 15.29657 Meter <-- Height of Pentagon
(Calculation completed in 00.005 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 16 Height of Pentagon Calculators

Height of Pentagon given Area using Interior Angle
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
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
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
Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
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
Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon given Diagonal
Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Width
Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Inradius using Interior Angle
Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
Height of Pentagon
Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
Height of Pentagon given Circumradius using Interior Angle
Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
Height of Pentagon given Perimeter
Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
Height of Pentagon given Circumradius using Central Angle
Height of Pentagon = Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon given Inradius using Central angle
Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5)))
Height of Pentagon = sqrt(5)*Inradius of Pentagon

## Height of Pentagon given Area using Central Angle Formula

Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
h = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*A)/5))/(2*sin(pi/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 using Central Angle?

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

How to calculate Height of Pentagon given Area using Central Angle using this online calculator? To use this online calculator for Height of Pentagon given Area using Central Angle, enter Area of Pentagon (A) and hit the calculate button. Here is how the Height of Pentagon given Area using Central Angle calculation can be explained with given input values -> 15.29657 = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*170)/5))/(2*sin(pi/5)).

### FAQ

What is Height of Pentagon given Area using Central Angle?
The Height of Pentagon given Area using Central Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its area and central angle and is represented as h = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*A)/5))/(2*sin(pi/5)) or Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/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 using Central Angle?
The Height of Pentagon given Area using Central Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its area and central angle is calculated using Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5)). To calculate Height of Pentagon given Area using Central Angle, 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*(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 = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*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 = 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) Let Others Know