Area of Pentagon given Height using Interior Angle Calculator

✖Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.ⓘ Height of Pentagon [h]

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

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Area of Pentagon given Height using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))
A = (5*((h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))
This formula uses 1 Constants, 3 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)

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Height of Pentagon: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (5*((h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)) --> (5*((15*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))

Evaluating ... ...

A = 163.472068801206

STEP 3: Convert Result to Output's Unit

163.472068801206 Square Meter --> No Conversion Required

FINAL ANSWER

163.472068801206 ≈ 163.4721 Square Meter <-- Area of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

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

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< Area of Pentagon Calculators

Area of Pentagon

LaTeX Go Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))

Area of Pentagon given Edge Length using Central Angle

LaTeX Go Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))

Area of Pentagon given Circumradius using Interior Angle

LaTeX Go Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)

Area of Pentagon given Edge Length and Inradius

LaTeX Go Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon

Area of Pentagon given Height using Interior Angle Formula

LaTeX Go

Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))
A = (5*((h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(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 Area of Pentagon given Height using Interior Angle?

Area of Pentagon given Height using Interior Angle calculator uses Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)) to calculate the Area of Pentagon, The Area of Pentagon given Height using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using height and interior angle. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Height using Interior Angle using this online calculator? To use this online calculator for Area of Pentagon given Height using Interior Angle, enter Height of Pentagon (h) and hit the calculate button. Here is how the Area of Pentagon given Height using Interior Angle calculation can be explained with given input values -> 163.4721 = (5*((15*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)).

FAQ

What is Area of Pentagon given Height using Interior Angle?

The Area of Pentagon given Height using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using height and interior angle and is represented as A = (5*((h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)) or Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)). Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

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

The Area of Pentagon given Height using Interior Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using height and interior angle is calculated using Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5)). To calculate Area of Pentagon given Height using Interior Angle, you need Height of Pentagon (h). With our tool, you need to enter the respective value for Height 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 Area of Pentagon?

In this formula, Area of Pentagon uses Height of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))
Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)

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