Area of Decagon given Inradius Calculator

✖Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.ⓘ Inradius of Decagon [r_i]

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✖Area of Decagon is the amount of 2-dimensional space occupied by the Decagon.ⓘ Area of Decagon given Inradius [A]

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Area of Decagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5)))
A = 5/2*(2*r_i)^2/sqrt(5+(2*sqrt(5)))
This formula uses 1 Functions, 2 Variables

Functions Used

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

Area of Decagon - (Measured in Square Meter) - Area of Decagon is the amount of 2-dimensional space occupied by the Decagon.
Inradius of Decagon - (Measured in Meter) - Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Decagon: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 5/2*(2*r_i)^2/sqrt(5+(2*sqrt(5))) --> 5/2*(2*15)^2/sqrt(5+(2*sqrt(5)))

Evaluating ... ...

A = 731.069316524039

STEP 3: Convert Result to Output's Unit

731.069316524039 Square Meter --> No Conversion Required

FINAL ANSWER

731.069316524039 ≈ 731.0693 Square Meter <-- Area of Decagon

(Calculation completed in 00.004 seconds)

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< Area of Decagon Calculators

Area of Decagon given Diagonal across Three Sides

LaTeX Go Area of Decagon = 5/2*sqrt(5+(2*sqrt(5)))*((2*Diagonal across Three Sides of Decagon)/sqrt(14+(6*sqrt(5))))^2

Area of Decagon given Diagonal across Five Sides

LaTeX Go Area of Decagon = 5/2*sqrt(5+(2*sqrt(5)))*(Diagonal across Five Sides of Decagon/(1+sqrt(5)))^2

Area of Decagon given Diagonal across Four Sides

LaTeX Go Area of Decagon = 5/2*(Diagonal across Four Sides of Decagon)^2/sqrt(5+(2*sqrt(5)))

Area of Decagon

LaTeX Go Area of Decagon = 5/2*sqrt(5+(2*sqrt(5)))*Side of Decagon^2

Area of Decagon given Inradius Formula

LaTeX Go

Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5)))
A = 5/2*(2*r_i)^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 Inradius?

Area of Decagon given Inradius calculator uses Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))) to calculate the Area of Decagon, The Area of Decagon given Inradius formula is defined as the measure of the total 2d space that the surface of the object occupies of a Decagon, calculated using its inradius. Area of Decagon is denoted by A symbol.

How to calculate Area of Decagon given Inradius using this online calculator? To use this online calculator for Area of Decagon given Inradius, enter Inradius of Decagon (r_i) and hit the calculate button. Here is how the Area of Decagon given Inradius calculation can be explained with given input values -> 731.0693 = 5/2*(2*15)^2/sqrt(5+(2*sqrt(5))).

FAQ

What is Area of Decagon given Inradius?

The Area of Decagon given Inradius formula is defined as the measure of the total 2d space that the surface of the object occupies of a Decagon, calculated using its inradius and is represented as A = 5/2*(2*r_i)^2/sqrt(5+(2*sqrt(5))) or Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))). Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

How to calculate Area of Decagon given Inradius?

The Area of Decagon given Inradius formula is defined as the measure of the total 2d space that the surface of the object occupies of a Decagon, calculated using its inradius is calculated using Area of Decagon = 5/2*(2*Inradius of Decagon)^2/sqrt(5+(2*sqrt(5))). To calculate Area of Decagon given Inradius, you need Inradius of Decagon (r_i). With our tool, you need to enter the respective value for Inradius of Decagon 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 Decagon?

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

Area of Decagon = 5/2*sqrt(5+(2*sqrt(5)))*Side of Decagon^2
Area of Decagon = 5/2*sqrt(5+(2*sqrt(5)))*(Diagonal across Five Sides of Decagon/(1+sqrt(5)))^2
Area of Decagon = 5/2*(Diagonal across Four Sides of Decagon)^2/sqrt(5+(2*sqrt(5)))

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