Height of Pentagon given Area using Interior Angle Calculator

✖The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.ⓘ Area of Pentagon [A]

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✖Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.ⓘ Height of Pentagon given Area using Interior Angle [h]

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Height of Pentagon given Area using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
h = sqrt((4*tan(pi/5)*A)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
This formula uses 1 Constants, 4 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., 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., 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((4*tan(pi/5)*A)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi) --> sqrt((4*tan(pi/5)*170)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)

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 00.020 seconds)

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Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

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< Height of Pentagon Calculators

Height of Pentagon given Edge Length using Central Angle

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

Height of Pentagon given Circumradius using Central Angle

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

Height of Pentagon given Inradius using Central angle

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

Height of Pentagon given Circumradius and Inradius

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

Height of Pentagon given Area using Interior Angle Formula

LaTeX 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)
h = sqrt((4*tan(pi/5)*A)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)

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 Interior Angle?

Height of Pentagon given Area using Interior Angle calculator 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 calculate 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 calculate Height of Pentagon given Area using Interior Angle using this online calculator? To use this online calculator for Height of Pentagon given Area using Interior Angle, enter Area of Pentagon (A) and hit the calculate button. Here is how the Height of Pentagon given Area using Interior Angle calculation can be explained with given input values -> 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).

FAQ

What is Height of Pentagon given Area using Interior Angle?

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 and is represented as h = sqrt((4*tan(pi/5)*A)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi) or 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). 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 Interior Angle?

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 is calculated using 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 calculate Height of Pentagon given Area using Interior 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 3 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)))

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