Area of Hexadecagon given Diagonal across Seven Sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)
A = 4*(d7*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)
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)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
Variables Used
Area of Hexadecagon - (Measured in Square Meter) - Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.
Diagonal across Seven Sides of Hexadecagon - (Measured in Meter) - Diagonal across Seven Sides of Hexadecagon is a straight line joining two non-adjacent vertices across seven sides of Hexadecagon.
STEP 1: Convert Input(s) to Base Unit
Diagonal across Seven Sides of Hexadecagon: 25 Meter --> 25 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = 4*(d7*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16) --> 4*(25*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)
Evaluating ... ...
A = 497.280918449145
STEP 3: Convert Result to Output's Unit
497.280918449145 Square Meter --> No Conversion Required
FINAL ANSWER
497.280918449145 497.2809 Square Meter <-- Area of Hexadecagon
(Calculation completed in 00.004 seconds)

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12 Area of Hexadecagon Calculators

Area of Hexadecagon given Circumradius
Go Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Seven Sides
Go Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Three Sides
Go Area of Hexadecagon = 4*(Diagonal across Three Sides of Hexadecagon*sin(pi/16)/sin((3*pi)/16))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Five Sides
Go Area of Hexadecagon = 4*(Diagonal across Five Sides of Hexadecagon*sin(pi/16)/sin((5*pi)/16))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Four Sides
Go Area of Hexadecagon = 4*(Diagonal across Four Sides of Hexadecagon*sin(pi/16)/sin((4*pi)/16))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Six Sides
Go Area of Hexadecagon = 4*(Diagonal across Six Sides of Hexadecagon*sin(pi/16)/sin((3*pi)/8))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Two Sides
Go Area of Hexadecagon = 4*(Diagonal across Two Sides of Hexadecagon*sin(pi/16)/sin(pi/8))^2*cot(pi/16)
Area of Hexadecagon given Inradius
Go Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16)
Area of Hexadecagon given Diagonal across Eight Sides
Go Area of Hexadecagon = 4*(Diagonal across Eight Sides of Hexadecagon*sin(pi/16))^2*cot(pi/16)
Area of Hexadecagon given Perimeter
Go Area of Hexadecagon = 4*(Perimeter of Hexadecagon/16)^2*cot(pi/16)
Area of Hexadecagon given Height
Go Area of Hexadecagon = 4*Height of Hexadecagon^2*tan(pi/16)
Area of Hexadecagon
Go Area of Hexadecagon = 4*Side of Hexadecagon^2*cot(pi/16)

Area of Hexadecagon given Diagonal across Seven Sides Formula

Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)
A = 4*(d7*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)

What is a Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture.

How to Calculate Area of Hexadecagon given Diagonal across Seven Sides?

Area of Hexadecagon given Diagonal across Seven Sides calculator uses Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16) to calculate the Area of Hexadecagon, The Area of Hexadecagon given Diagonal across Seven Sides formula is defined as the amount or quantity of space occupied by a Hexadecagon in the plane, calculated using a diagonal across seven sides. Area of Hexadecagon is denoted by A symbol.

How to calculate Area of Hexadecagon given Diagonal across Seven Sides using this online calculator? To use this online calculator for Area of Hexadecagon given Diagonal across Seven Sides, enter Diagonal across Seven Sides of Hexadecagon (d7) and hit the calculate button. Here is how the Area of Hexadecagon given Diagonal across Seven Sides calculation can be explained with given input values -> 497.2809 = 4*(25*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16).

FAQ

What is Area of Hexadecagon given Diagonal across Seven Sides?
The Area of Hexadecagon given Diagonal across Seven Sides formula is defined as the amount or quantity of space occupied by a Hexadecagon in the plane, calculated using a diagonal across seven sides and is represented as A = 4*(d7*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16) or Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16). Diagonal across Seven Sides of Hexadecagon is a straight line joining two non-adjacent vertices across seven sides of Hexadecagon.
How to calculate Area of Hexadecagon given Diagonal across Seven Sides?
The Area of Hexadecagon given Diagonal across Seven Sides formula is defined as the amount or quantity of space occupied by a Hexadecagon in the plane, calculated using a diagonal across seven sides is calculated using Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16). To calculate Area of Hexadecagon given Diagonal across Seven Sides, you need Diagonal across Seven Sides of Hexadecagon (d7). With our tool, you need to enter the respective value for Diagonal across Seven Sides of Hexadecagon 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 Hexadecagon?
In this formula, Area of Hexadecagon uses Diagonal across Seven Sides of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Area of Hexadecagon = 4*Side of Hexadecagon^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Eight Sides of Hexadecagon*sin(pi/16))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Six Sides of Hexadecagon*sin(pi/16)/sin((3*pi)/8))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Five Sides of Hexadecagon*sin(pi/16)/sin((5*pi)/16))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Three Sides of Hexadecagon*sin(pi/16)/sin((3*pi)/16))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Two Sides of Hexadecagon*sin(pi/16)/sin(pi/8))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Perimeter of Hexadecagon/16)^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Diagonal across Four Sides of Hexadecagon*sin(pi/16)/sin((4*pi)/16))^2*cot(pi/16)
  • Area of Hexadecagon = 4*Height of Hexadecagon^2*tan(pi/16)
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