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Area of Decagon given diagonal across four sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
A = (5/2)*((d4/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Diagonal across four sides - Diagonal across four sides is a straight line joining two opposite sides which is across four sides of the given polygon. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Diagonal across four sides: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = (5/2)*((d4/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) --> (5/2)*((9/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
Evaluating ... ...
A = 65.7962384871635
STEP 3: Convert Result to Output's Unit
65.7962384871635 Square Meter --> No Conversion Required
FINAL ANSWER
65.7962384871635 Square Meter <-- Area
(Calculation completed in 00.000 seconds)

10+ Area of Decagon Calculators

Area of Decagon given diagonal across three sides
area = (5/2)*(((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given diagonal across two sides
area = (5/2)*(((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given diagonal across four sides
area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given height
area = (5/2)*((Height/((sqrt(5+2*sqrt(5)))))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given diagonal across five sides
area = (5/2)*((Diagonal across five sides/((1+sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given circumradius
area = (5/2)*(((2*Radius)/(1+sqrt(5)))^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given perimeter
area = (5/2)*((Perimeter/10)^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon
area = (5/2)*(Side^2)*(sqrt(5+2*sqrt(5))) Go
Area of Decagon given side length and central angle
area = (5*(Side)^2)/(2*tan(Angle A/2)) Go
Area of Decagon given inradius and side length
area = 5*Side*Inradius Go

Area of Decagon given diagonal across four sides Formula

area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
A = (5/2)*((d4/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))

What is a decagon?

Decagon is a polygon with ten sides and ten vertices. A decagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. A convex decagon has none of its interior angles greater than 180°. To the contrary, a concave decagon (or polygon) has one or more of its interior angles greater than 180°. A decagon is called regular when its sides are equal and also its interior angles are equal.

How to Calculate Area of Decagon given diagonal across four sides?

Area of Decagon given diagonal across four sides calculator uses area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) to calculate the Area, The Area of decagon given diagonal across four sides formula is defined as measure of the total area that the surface of the object occupies of a decagon , where area = area of decagon, diagonal = diagonal across four sides of decagon. Area and is denoted by A symbol.

How to calculate Area of Decagon given diagonal across four sides using this online calculator? To use this online calculator for Area of Decagon given diagonal across four sides, enter Diagonal across four sides (d4) and hit the calculate button. Here is how the Area of Decagon given diagonal across four sides calculation can be explained with given input values -> 65.79624 = (5/2)*((9/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))).

FAQ

What is Area of Decagon given diagonal across four sides?
The Area of decagon given diagonal across four sides formula is defined as measure of the total area that the surface of the object occupies of a decagon , where area = area of decagon, diagonal = diagonal across four sides of decagon and is represented as A = (5/2)*((d4/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))) or area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))). Diagonal across four sides is a straight line joining two opposite sides which is across four sides of the given polygon.
How to calculate Area of Decagon given diagonal across four sides?
The Area of decagon given diagonal across four sides formula is defined as measure of the total area that the surface of the object occupies of a decagon , where area = area of decagon, diagonal = diagonal across four sides of decagon is calculated using area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5))). To calculate Area of Decagon given diagonal across four sides, you need Diagonal across four sides (d4). With our tool, you need to enter the respective value for Diagonal across four sides 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?
In this formula, Area uses Diagonal across four sides. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • area = 5*Side*Inradius
  • area = (5*(Side)^2)/(2*tan(Angle A/2))
  • area = (5/2)*(Side^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*((Diagonal across five sides/((1+sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*((Diagonal across four sides/(sqrt(5+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*(((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*(((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*((Perimeter/10)^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*((Height/((sqrt(5+2*sqrt(5)))))^2)*(sqrt(5+2*sqrt(5)))
  • area = (5/2)*(((2*Radius)/(1+sqrt(5)))^2)*(sqrt(5+2*sqrt(5)))
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