Area of Nonagon given Diagonal across Three Sides Calculator

✖Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon.ⓘ Diagonal across Three Sides of Nonagon [d₃]

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✖The Area of Nonagon is the amount of two-dimensional space taken up by the Nonagon.ⓘ Area of Nonagon given Diagonal across Three Sides [A]

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Area of Nonagon given Diagonal across Three Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Nonagon = 9*Diagonal across Three Sides of Nonagon^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9))
A = 9*d₃^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9))
This formula uses 1 Constants, 2 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)

Variables Used

Area of Nonagon - (Measured in Square Meter) - The Area of Nonagon is the amount of two-dimensional space taken up by the Nonagon.
Diagonal across Three Sides of Nonagon - (Measured in Meter) - Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Three Sides of Nonagon: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 9*d₃^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)) --> 9*20^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9))

Evaluating ... ...

A = 385.672565811924

STEP 3: Convert Result to Output's Unit

385.672565811924 Square Meter --> No Conversion Required

FINAL ANSWER

385.672565811924 ≈ 385.6726 Square Meter <-- Area of Nonagon

(Calculation completed in 00.004 seconds)

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< Area of Nonagon Calculators

Area of Nonagon given Height

LaTeX Go Area of Nonagon = (((3*sin(pi/9)*Height of Nonagon)/(1+cos(pi/9)))^2)/(tan(pi/9))

Area of Nonagon given Circumradius

LaTeX Go Area of Nonagon = 9/2*Circumradius of Nonagon^2*sin(2*pi/9)

Area of Nonagon given Perimeter

LaTeX Go Area of Nonagon = (Perimeter of Nonagon^2*cot(pi/9))/36

Area of Nonagon given Inradius

LaTeX Go Area of Nonagon = 9*Inradius of Nonagon^2*tan(pi/9)

Area of Nonagon given Diagonal across Three Sides Formula

LaTeX Go

Area of Nonagon = 9*Diagonal across Three Sides of Nonagon^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9))
A = 9*d₃^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9))

What is Nonagon?

A Nonagon is a polygon with nine sides and nine angles. The term ‘nonagon’ is a hybrid of the Latin word ‘nonus’ meaning nine and the Greek word ‘gon’ meaning sides. It is also known as ‘enneagon’, derived from the Greek word ‘enneagonon’, also meaning nine.

How to Calculate Area of Nonagon given Diagonal across Three Sides?

Area of Nonagon given Diagonal across Three Sides calculator uses Area of Nonagon = 9*Diagonal across Three Sides of Nonagon^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)) to calculate the Area of Nonagon, The Area of Nonagon given Diagonal across Three Sides formula is defined as the amount of 2-dimensional space occupied by Nonagon in space, calculated using the diagonal across three sides. Area of Nonagon is denoted by A symbol.

How to calculate Area of Nonagon given Diagonal across Three Sides using this online calculator? To use this online calculator for Area of Nonagon given Diagonal across Three Sides, enter Diagonal across Three Sides of Nonagon (d₃) and hit the calculate button. Here is how the Area of Nonagon given Diagonal across Three Sides calculation can be explained with given input values -> 385.6726 = 9*20^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)).

FAQ

What is Area of Nonagon given Diagonal across Three Sides?

The Area of Nonagon given Diagonal across Three Sides formula is defined as the amount of 2-dimensional space occupied by Nonagon in space, calculated using the diagonal across three sides and is represented as A = 9*d₃^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)) or Area of Nonagon = 9*Diagonal across Three Sides of Nonagon^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)). Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon.

How to calculate Area of Nonagon given Diagonal across Three Sides?

The Area of Nonagon given Diagonal across Three Sides formula is defined as the amount of 2-dimensional space occupied by Nonagon in space, calculated using the diagonal across three sides is calculated using Area of Nonagon = 9*Diagonal across Three Sides of Nonagon^2*cos(pi/9)*sin(pi/9)/(4*sin(3*pi/9)*sin(3*pi/9)). To calculate Area of Nonagon given Diagonal across Three Sides, you need Diagonal across Three Sides of Nonagon (d₃). With our tool, you need to enter the respective value for Diagonal across Three Sides of Nonagon 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 Nonagon?

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

Area of Nonagon = 9/2*Circumradius of Nonagon^2*sin(2*pi/9)
Area of Nonagon = (((3*sin(pi/9)*Height of Nonagon)/(1+cos(pi/9)))^2)/(tan(pi/9))
Area of Nonagon = 9*Inradius of Nonagon^2*tan(pi/9)

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